Cantrips only scale with character level because the rules on pg 164 say so.
There is nothing on pages 163 and 164 that says Warlock Invocation prerequisites are character level, so they aren't.
I will repeat: The rules for multiclassing are on pages 163 and 164. They are variant rules. The rest of the rules are not written to refer to the multiclassing rules. They are not part of the base game.