Hi,
this is not possible, there is only one cache for all users and deleting it means it is delete from all users, the whole point of cache is that you store something when one user executes some command, so that when next user does the same thing he will get those results faster. To be able to clean cache just for one user you would need to also store it for each user separately, which usually means that you loose all speed gains and so the whole point of cache.
Enabling cache on search type User only means you are caching results when someone searches for users.