There are several ways a person who Joe has not explicitly made aware of the situation can become aware of it, so long as Joe does not prevent this from happening.
Some of Joe's comments may require others to observe changes in the universe rather than have it appear to always have been so:
"There was a park here a minute ago, but now it's an airport."
Because for the statement to be true, an observer would have to know that the previous state was true, and would surely remember it. Memory alteration would cause the statement to be false for that person.
If Joe's comments are not contradictory of present reality, no rewriting will take place and his ability to state what will happen would be deducable due to probability.
"I'm going to get four straight flushes in a row!
"That dog is going to jump over the car, land in a roll, and come up doing a moonwalk while singing showtunes!"
"Everyone who sees this answer is going to upvote it!"
On seeing anything incredible happen right after he said it, it would immediately draw attention to how unbelievably coincidental it was. At first it would appear to be predictive rather than causative, but that could eventually be figured out.
Even mundane comments about future events will tip people off that Joe has an uncanny ability to state what's going to happen. One or two comments would not be surprising, and from there they could question the nature of the ability and eventually findbut if everything he said always turned out through experimentation itsto be true naturethat would be enough for people around Bob to become curious and eventually discover his ability.