Typically, while docked at a Starfleet/Federation facility, it's not 100% necessary to have a crew presence on the bridge - in a lot of cases, the crew of ships (especially those the size of
Peregrine) might take this brief stop at the Starbase as an opportunity to get in some "off ship" R&R - Starbase personnel (i.e a Starfleet Security attachment posted to the base) can easily and readily be "substituted in" to relieve the ship's crew. On the other hand, each ship's TAC/SEC officer likely has their own methods and, quite possibly, would dictate that
at least one ship-side security officer man/guard the bridge.
That said, I don't think that we're really going to be at SB118 for too long. So I doubt we see a full scale exodus for shore leave. You'd have to talk to the TAC Chief to be sure about watches.
Also... no, in the instance you refer to, "Mister" was not an insult. Perfectly fine and acceptable use of the term.