new guy here

I have this work on my university to make AI for chess, but pretty simple one. I implemented MiniMax algorithm already, but its terribly slow, so I decided to try out AlphaBeta pruning.
So I did some research on google of course, I understand how the algorithm should work, but I'm a bit confused about something:
Everywhere I see they say AlphaBeta goes to the first deepest node (leaf), and then evaluates that move and returns it to the parent node. But, as I can see, that is the ONLY time the move is evaluated (I mean only on deepest nodes), because every node that is more "up" from the deepest node doesn't evaluate it's move, it just takes alpha/beta value from its children...
Hope you understand what confuses me.
Looking forward to your replies and help!
Cheers!