No, you have to relinquish it to the King's control. I've been operating on the assumption that surrendering it to the King happens by default because it would be tedious to announce it constantly, but the turn you take it you can decide not to give it to the King if you wish.

Since it's an active decision for the person capturing the city or castle I've taken it for granted that there is leeway the same turn as the capture to move your forces out... say it happens before you officially turn the province over to the King. After that turn passes, however, those men are the King's if he wants them.

This is the first time the rule has been tested, however, so we should work things out for absolute certain before we proceed if it's going to cause conflict.