For Space Shuttle:
In the flight software, "tower clear" was defined as the end of the vertical rise phase when it was OK to start the Single Axis Rotation (aka "roll program"). This happened when the vehicle center of mass was at 376 feet above the Fischer Ellipsoid.
Source - Ascent Nominal I-Loads Definition and Verification (not online)
However, "tower clear" is a phony breakpoint in authority. For all practical purposes, MCC-Houston was in charge after SRB ignition.
A1-5 FLIGHT DIRECTOR AUTHORITY
A. THE FLIGHT DIRECTOR IS RESPONSIBLE
FOR OVERALL DIRECTION OF SHUTTLE FLIGHTS FROM SOLID ROCKET BOOSTER
(SRB) IGNITION UNTIL CREW EGRESS OR GSE COOLING ACTIVATION, WHICHEVER
OCCURS LATER:
- THE FLIGHT DIRECTOR IS RESPONSIBLE FOR REAL-TIME IMPLEMENTATION OF OPERATIONS WITHIN THE FRAMEWORK OF THE SHUTTLE OPERATING BASE
(REFERENCE (REF.) RULE {A1-2}, REAL-TIME OPERATING POLICY).
- THE FLIGHT DIRECTOR IS RESPONSIBLE FOR PROVIDING RECOMMENDATIONS AND/OR OPTIONS TO THE MMT FOR NEAR REAL-TIME DECISIONS WHEN OPERATING
OUTSIDE THE FRAMEWORK OF THE MISSION RULES OR THE SHUTTLE OPERATING
BASE.
Emphasis mine. Source: Space Shuttle Flight Rules paragraph A1-5
You will search in vain for any example of KSC talking to the crew or sending a command to the vehicle after SRB ignition.
For Apollo:
Not a complete answer but the flight rules are explicitly different and authority does transfer at tower clear.
Complete ground control of the space vehicle passes to the flight
director when the space vehicle reaches sufficient altitude to clear
the umbilical tower.
Apollo 11 Mission Rules rule 1-21