The exit receives control in AMODE(64) if the service was invoked in AMODE(64); otherwise the exit receives control in AMODE(31). If you have a callable service exit for a service which supports invocation by an AMODE(64) caller, once HCR7720 is installed, you should recode your exit to be sure it can handle being invoked in AMODE(64).
The exits can change the characteristics during their processing. However, the exits must return to ICSF with the same characteristics as on entry.