I'd guess that a plane is more likely to get some "rest" prior to its red-eye flight, not after. That is, an aircraft arrives in a West Coast city around 8 or 9 local time, then gets a two-hour or so break until the red-eye departs.

This cushion allows for some padding to get back on schedule in the event of earlier delays, thus preventing one day's poor ops from spilling into the next day. Certainly this isn't true in all cases, but I think it's far more likely that an arriving red-eye aircraft is immediately turned around to be a part of the first morning bank of flights.