Note that "32 minutes past the hour" is true whether you are referring to Eastern Time or UTC. Just the "hour" is different.
Because a program references UTC, does not mean that other times are not used. The main reference time for Apollo was GET.
The term “GET” (Ground Elapsed Time), used for manned U.S. spaceflights prior to the Space Shuttle, was referenced to “Range Zero,” the last integral second before liftoff. With the first launch of the Shuttle, NASA began using the term “MET” (Mission Elapsed Time), which begins at the moment of solid rocket booster ignition.
The ISS uses UTC but also local Houston and Moscow time. See the top bands in this example of the Onboard Short Term Plan Viewer
From What kind of time regiment/schedule do ISS astronauts have?