The problem made by The Truman show operators was not isolated rain. It is more fundamental than that.
As others have said, they taught Truman about the real world, and they taught him about fake worlds on tv shows. Then expected him not to discover that his life was more similar to a fake world than the real one? They taught Truman what a plane was, and then scared him away from using them by saying they are dangerous. Why tell him of the existence of planes in the first place?
They taught him that there was a world out there, and built a dome that blocked him off from it. They gave him a tv, so he would be expected to recognise a terrible, overdramatic tv plot - when his uncle twice removed comes back from the dead, claiming to have had amnesia, and actually be the heir to the Morgan family fortune, Morgan will realise that not only is he in a tv show, but the ratings are heading south. TV producers are bad at their job, and he will realise eventually, if he has tv to compare his life to.
People are inherently curious. They will explore the limits of their environment. If there is a dome, they will find it. If they have been taught that there is a 'rest of the world' out there, they will realise they are in a 'fake world'.
If the Morgan show crew take the same fundamental approach as the Truman show (he knows the world population is ~7 billion, he owns a car and a tv, can afford a plane ticket and reach an airport, and is contained within his world by a dome and 'coincidences' to keep him away from it, He will inevitably try so frequently to leave that the 'coincidences' become obvious conspiracy.
If they actually wanted Morgan to never realise he was in a tv show, they would need a much better way to stop him from leaving than relying on him not being curious, and the dome is a liability, not an asset.
Base the show in the middle of hostile and remote terrain, i.e. somewhere in Australia, near the border of SA, WA and NT. Don't build a stupid dome. Don't give the town an airport. If he leaves, that's not a problem. Tell both of the people who live within 24 hours drive not to freak out if he talks to them, and if he does drive for 4 days straight to reach Perth, Darwin or Adelaide, plenty of time to drill everyone in 'not messing up a conversation with him', and some time to stage a mugging and some other unpleasant events to make sure he doesn't enjoy his holiday.
The best way to stop him realising it is a tv show would be locate the town as above, but don't teach Morgan about the existence of any of the following items: Car, plane, train, T.V., computer, smartphone. This way, if he leaves the town, he will be dying of thirst before he reaches anywhere (and plenty of time for the town to send a rescue team to save him. Have the town mostly self sufficient, and bring in supplies by wagon (well, 99% of the way by truck and the last bit by wagon). This may make the TV show less realistic I suppose?