OK, not minimum separation but average separation.
No, it's the separation one would get, if trains were released every 90 seconds. I'm assuming uniform headways - (0, 90, 180, 270,...) not (0, 45, 225, 270,...). It's the function of the train supervision system to maintain proper headways, not the signal system. NYCT has a very crude supervision system (holding lights). Systems that approach or exceed 40 tph use the latest in 16th century technology - clocks.
If there are uniform headways, then train separation will be 6750 feet, if the trains are operating at 75 ft/sec. How close will the get, if station dwell time is 30 seconds and both acceleration and braking rates are 4 ft/sec2? N.B. one of the charms of NYCT is that service braking rate is 3.2 mph/sec (4.7 ft/sec2) whereas emergency braking rate is 3.0 mph/sec (4.4 ft/sec2).
As you noted it will take 703 feet and 18.75 sec for the train to stop. Let x = 0 be the front of the station and let T = 0 be the time that the leader is 703 feet from the front of the station and beginning to brake.
At T = 0 the leader will be at x = -703, travelling at 75 ft/sec and the follower will be at x = -7453, travelling at 75 ft/sec. The distance between the trains is 6750 feet.
At T = 18.75 the leader will be at x = 0, travelling at 0 ft/sec and the follower will be at x = -6046.75, travelling at 75 ft/sec. The distance between trains will be 6046.75 feet.
At T = 48.75 the leader will still be at x = 0, travelling at 0 ft/sec and the follower will be at x = -3796.75, travelling at 75 ft/sec. The distance between trains will be 3796.75 feet.
At T = 67.5 the leader will be at x = 703, travelling at 75 ft/sec and the follower will be at x = -2390.5, travelling at 75 ft/sec. The distance between trains will be 3093.5 feet.
At T = 90 the leader will be at x = 2390.5, travelling at 75 ft/sec and the follower will be at x = -703, travelling at 75 ft/sec. The distance between trains will be 3093.5 feet.
At T = 108.75 the leader will be at x = 3796.75, travelling at 75 ft/sec and the follower will be at x = 0, travelling at 0 ft/sec. The distance between trains will be 3796.75 feet.
At T = 138.75 the leader will be at 6046.75, travelling at 75 ft/sec and the follower will be at x = 0, travelling at 0 ft/sec. The distance between trains will be 6046.75 feet.
At T = 157.5 the leader will be at 7453, travelling at 75 ft/sec and the follower will be at 703 feet travelling at 75 ft/sec. The distance between trains will be 6750 feet.