Sometimes bettas just jump, but they do usually have a reason. My guess is maybe something startled him?
Are there any plants in the tank?
Do you have a sponge filter or similar?
Last water change size/time?
Definitely get a good tight lid.
Also consider adding a couple of dry oak leaves to the water. They'll tint it with tannins. Tannins are supposed to help fish heal, and the slight golden tinting should make him happy. The leaching of tannins into the water will be slow and shouldn't bother him, and at worse it will do nothing. Find some dry, fallen oak leaves in a pesticide-free place, wash them off in hot water, and add them. Maybe 4-6 of them... One per gallon is good. Tinted brown water indicates tannins releasing, not anything bad.