Thank you for the replies, everyone. I'm sort of glad I wasn't just being paranoid. I'll try to follow Taon's method and see if I can still fully enjoy the spillover stamina. Otherwise, I guess I'll need to start planning and calculating when close to leveling up, to make sure I've expended as much stamina as possible beforehand.

This is probably the first game with energy/stamina spillover I've come across with such a problem. Then again, I've only started playing mobile and browser games since 2 years ago.