Here's your 7110.65 language in the Air Traffic Controller Handbook:

2-1-27 TCAS Resolution Advisories

a. When an aircraft under your control jurisdiction informs you that it is responding to a TCAS Resolution Advisory (RA), do not issue control instructions that are contrary to the RA procedure that a crew member has advised you that they are executing. Provide safety alerts regarding terrain or obstructions and traffic advisories for the aircraft responding to the RA and all other aircraft under your control jurisdiction, as appropriate.
b. Unless advised by other aircraft that they are also responding to a TCAS RA, do not assume that other aircraft in the proximity of the responding aircraft are involved in the RA maneuver or are aware of the responding aircraft's intended maneuvers. Continue to provide control instructions, safety alerts, and traffic advisories as appropriate to such aircraft.
c. Once the responding aircraft has begun a maneuver in response to an RA, the controller is not responsible for providing standard separation between the aircraft that is responding to an RA and any other aircraft, airspace, terrain or obstructions. Responsibility for standard separation resumes when one of the following conditions are met:
1. The responding aircraft has returned to its assigned altitude, or
2. A crew member informs you that the TCAS maneuver is completed and you observe that standard separation has been reestablished, or
3. The responding aircraft has executed an alternate clearance and you observe that standard separation has been reestablished.
NOTE -
1 - AC 120-55A suggests pilots use the following phraseology to notify controllers during TCAS events. When a TCAS RA may affect an ATC clearance, inform ATC when beginning the maneuver or as soon as workload permits:
EXAMPLE -
1 - "New York Center, United 321, TCAS climb."
NOTE -
2 - When the RA has been resolved, the flight crew should advise ATC they are retuning to their previously assigned clearance or subsequent amended clearance:
EXAMPLE -
2 - "New York Center, United 321, clear of conflict, returning to assigned altitude."