As far as I'm aware, there is no need to record the actual times of departure and arrival. The total flight time (i.e. chocks off to chocks on) and the date of departure (GMT/UTC) is all that is required.
Having said that, I have always recorded the times of dep and arr probably because my first logbook had columns for them!
I too was surprised when I was hour building in Arizona in 1975 and some of my flights arrived after midnight z.
Arizona is GMT-8, so a flight in the late afternoon (1500-1630L) would be recorded as 2300-0030z.