Regarding how ATC respond to TCAS RA's it is 'good practice' not to give any vertical avoiding action once an RA is notified. (Having said that, in the proverbial heat of the situation I'm sure some controllers may try to climb/descend an a/c back to where they thought it should've been.
Traffic information is encouraged but we're encouraged only to give avoiding action in the horizontal plane and wait until you report 'back under my control'.