In an earlier episode, it was stated that if Jeannie married her master, she would lose her powers. Jeannie was happy with that, but Tony changed his mind when he found out their children could be genies.
When they eventually did marry in Season 5, Jeannie did not lose her powers, as they were still there right up to the final episode.
She also still had powers in the 15 years later spin off.
That is one of many well-known contradictions within the show.
What you have to do is to forget about it, and remember that back then, the concept of a "show bible" didn't exist. Continuity people were common on movies, but not on TV shows, unless they had the budget for them. IDoJ did not.
It was also common for writers to work for several different shows at the same time. So, they'd have to keep various facts straight in their heads, if they knew them at all. Presumably, they were either given some basic facts about the characters, or they watched episodes to get an idea and feel for the show. I would hope that Sheldon approved their stories beforehand, but the inconsistencies tend to show even he didn't care as much.
As for the reunion movies, almost none of their content matched the original show, other than Jeannie being a djinni and blinking to use her power. They changed her age, the sound of her magic, her harem outfits, and even her character to some extent. Best to forget those entirely
In an earlier episode, it was stated that if Jeannie married her master, she would lose her powers. Jeannie was happy with that, but Tony changed his mind when he found out their children could be genies.
When they eventually did marry in Season 5, Jeannie did not lose her powers, as they were still there right up to the final episode.
She also still had powers in the 15 years later spin off