Hmm, I definetly had the latest version ( or was there another update since the airman stage was introduced?)
And I had other characters jumping fine on the key that did nothing on Sniper Joe,
I´ll redownload it tonight and check it again.
Edit:
Tried it again and the error could be, that I had the jump button mapped to triangle and cross.
I tried to skip the mesage that says "just press the buttons shown" with the jump key so
that I accidentally missmapped the keys.
Edit2:
Did a clean reconfig and sniper joe jumps like he should, when you press the top action key and the bottom key at the same time he won´t jump, so that really was it.