I don't have any divided tanks, but I did have a tank without a lid at one time (there's one on there now)... and I lost a gal... hopped right out the 2nd day.
Back when I had a divided 2.5, I had this female (still have her actually) and she would jump over the divider onto the males side every morning when I'd remove the lid to feed them
I've never kept my bettas in divided tanks, and the only time I've had bettas jump was when they were being acclimatized to the tank (they jumped from the bag of water into the tank, luckily).