Diavolo can move inside of Dio Time stop
The reason for that is something the manga show us well: Stands that naturally act outside the conventional time and space rules can move in the time stop.
Just take a look who was able to do it:
Star platinum ( while time stopping, when Star Platinum time gets over, him and jotaro freeze as well as anyone — besides Jotaro still being able to think during the time stop —, wich means their existence lost the " outsider time" condition)
Tusk Act 4 ( Wich is one stand able to distort time and space because of the rotation power, he's naturally otuside of conventional time and space rules ).
Diavolo fits the same logic that made Tusk able to do it. King Crimson and Diavolo existence are complete independent of time, if Dio stop time before Diavolo erases it, Diavolo could still move or, in the worst scenario, just King Crimson should ( but it couldn't make a sense because Diavolo explicitly tells us that he's able to move outside time thanks to KC)