Well, the starting datetime at the beginning of execution in the container is whatever you set it to:

$ hermit run --epoch=2022-01-01T00:00:00Z /bin/date

Fri Dec 31 16:00:00 PST 2021

We, somewhat eccentrically, put it in last millennium by default. It used to default to the original Unix epoch back in 12/31/1969, but that was causing some software to be very unhappy ;-).

The reproducibility guarantee is that the behavior of the program is a deterministic function of its initial configuration. The epoch setting is one aspect of that initial configuration (as are file system inputs, RNG seeds, etc).