OK. Problem solved however I still don't fully understand what's wrong.
After many tests I discovered the problem was one of the conditions of the event set for Idle. Take a look at the below screenshot:
If the circled condition is turned off (toggled) I get the one frame climbing animation problem. If the Player 1 "Move Up" is down
condition is active in the third step, than all is fine.
From my point of view however it's a weird behavior.