Without some significant immediate effect, such as erasing some of the obvious signs of aging (wrinkles, liver spots, etc) within a short period of time, the life extension properties won't be noticed at all for several decades, if at all.
After 10 years, a few people will have lived ~5 years longer than they otherwise would have. That's well within the normal variation and will go completely unnoticed.
20 years after the fruit is introduced a larger group of people will have lived an extra 10 years. Since they were already in the 'very old' group at the start, and many of their peers have succumbed to illness, pre-existing conditions and so on. While the age numbers are starting to reach a statistical threshold, the numbers are still quite small. People might start to notice that a lot more people are living past 100 years, but the average age of death has been increasing for centuries so it's not really big enough to be interesting.
30 years, and now we're getting to interesting territory. The record for the oldest person in the world has been broken a few times. The average age of the top 100 oldest people in the world goes from ~115 years (I know, right?) to > 120 years. This is a major statistical anomaly, but one that might not be noticed by anyone not actively studying the statistics of age.
40 years on and the odds are fairly high that a person will reach 130 years of age for the first time. People start to take note. Studies are begun to identify the causes, but with 40 years of medical advances and so on it's going to take a while before someone even realizes that the numbers started 4 decades back. Rigorous statistical analysis will identify the time-frame of the cause, then a bunch of studies will be done to identify what changed around that time. With thousands of factors to consider it's going to take a while. They'll probably find it eventually, but it might be 50 years after introduction before it becomes clear that the fruit is the source of the increased lifespan.
There are a few ways this can go horribly wrong.
Meanwhile, the fruit has become so valuable as a desirable food crop that the agricultural industries have already made a number of changes to the genetics of the plant. They've made the fruit larger, grow faster and so on. In the process of breeding the plant for these desirable traits they destroyed the genetic sequence that produced the specific enzyme that increases the lifespan. While the original genome still exists in a small number of plants, the commercially modified version is by far the most common. Only a handful of small fruit farms - specializing in the purest of organic, natural foods - still produce the original fruits, and only their customers are getting the benefits. Suddenly that anomaly in the age statistics flattens out and drops back to historical norms, with only a tiny increase over historic trends.
Having failed to identify the cause, most of the researchers will eventually be moved to more profitable work.
If this happens then it's going to be a long, long time before anyone discovers that the original fruit, now only available from a handful of organic hobby farms around the world, is anything special. Probably by accident.
Maybe in the first few years someone starts using the fruit as feed for lab animals and notices that mice who eat the fruit as part of their diet tend to have fewer degenerative diseases and live longer on average. They start a study, feeding various parts and amounts of the fruit to different groups of rats and figure out the most effective numbers. They end up with a 6 year old mouse, twice the average maximum age of a mouse in lab conditions.
Of course humans being what they are the next thing that happens is that someone publishes a detailed - and entirely false - paper claiming that the plant is actually toxic to some fraction of the population and is in fact to blame for the increase in some obscure health condition. Governments move to restrict the sale of the fruit, eventually banning it altogether as a foodstuff. Federal troops start burning crops again, and nobody really complains because it's just some odd fruit that is nice and all, but if it's actually toxic then better to get rid of it.
A few pharmaceutical companies spend billions of dollars trying to isolate the compound, while a small number of powerful, wealthy people are the only ones left in the world who have access to the raw fruit. Within a decade the only plants left are the ones on special production farms where the fruit is grown for 'medical research' purposes. The largest pharmaceutical companies begin to sell age extension products at a price that only the top 0.5 percent of the population - and the CEO of the pharmaceutical company - can even consider. It's the most expensive fruit juice the world has ever known.
Letting the effects stack up until they become statistically noticeable is going to take a long time - at least 20 years before it becomes significant enough to pique someone's interest. To get it noticed earlier you're going to need to see the effects either on a population of short-lived animals (like the lab mice) or in an existing population of humans that have been eating the fruit for a long time. Let's say there are native tribes who live in the area the fruit was found, but don't have much interaction outside of their tribal groups. They actually live for well over 150 years on average, but nobody has ever been able to figure that out. Eventually an anthropologist studying one of the tribes figures out that some of the village elders are way over 100 after they start talking to him about some major event they witnessed and he figures out how long ago it was.
This leads to studies being conducted and the world finds out about the small tribe in Papua New Guinea or the Amazon Basin that lives to be 150 years old. Researchers spend years trying to work out why it is happening, and eventually figure out that the ones who live the longest are the ones who regularly eat the fruit. The ones who don't like the taste or don't have access to the fruit due to geography have normal life spans for other tribal groups in the region.
By the time the cause is discovered it is too late for the world powers to cover it up. The fruit is already out there, exported to various parts of the world as a new foodstuff. It grows well in a variety of environments, appeals to the majority of people and becomes a favorite food for many. Juice from the fruit starts to out-sell orange juice, and orange-producing locations in various parts of the world transition to producing the new fruit. Before anybody knows about the medical properties of the fruit - and the juice as well - it has become far too common to be suppressed.
Within 50 years the average age of death from age-related causes has risen significantly. People are staying fit and healthy for much longer, average retirement age has gone up 20 years and the world's population has risen by 80% over even the most generous estimates, and it's getting worse. World poverty levels rise out of control, infrastructure designed for the prior predictions proves insufficient and systems fail. Food production can't keep pace with the population growth. Disease and famine claim millions of people a day, violence accounts for millions more, and still the population climbs. Some few people try to save the world from itself, but end up just causing more problems.
Pretty soon the world starts looking like Mad Max had a hate child with Idiocracy. Brave New World was the midwife.
I'm sure there are some good ways this could go, but I'm really not feeling positive about it. Perhaps a borderline misanthrope is not the best source of ideas here. ;D