The ability does absolutely nothing if the opponent can just move away. You're climbing on them you go with them.
The entire archetype is written with a few gaps missing in the mechanics.
I disagree with BNW. While surely this is a deficit in the rules, they mention nothing to stop a creature from moving away so that the vexing dodger isn't adjacent or occupying the same space.
It's unclear what happens exactly.
It could stay on with no check required, but that seems to good.
It could be left behind with no check allowed, although moving away would provoke. It might be possible to make something happen so that you can follow it if it moves away.
The last option is between those two where a check is made determine if the rogue stays on. This is the most reasonable, but no real guidance is given to determine how it should be run.
There's also the gap of there being no mechanism for the creature being climbed to remove or escape the rogue climbing them. The rogue only need make a climb check vs CMD, so there isn't much a creature can do to proactively try to remove the rogue from climbing them, though there probably should be. Like a CMB check to knock them off perhaps.
It also doesn't cover situations like "what if the big monster grapples the vexing dodger?" Does the dodger still count as climbing? Is the monster even allowed to attempt to grapple?
So I guess the one thing we can agree on is, this archetype has a lot of problems.