I have had plenty of 5, 6, 7am duty on at FBO without or with a trip hours later.
Have called and asked to stay at the hotel, and have been told no, we need you at the FBO for coverage
So it does happen in the mornings
I will say it seems to be becoming less the normal than it was before, before it was pretty routine.

End of day, it depends on what time of the day it is and how much duty you have left.
Been done at 1pm with a hotel booked and only 5 hours of duty done, and been told to hang out, call back.
Been done at 5pm and only 5 hours of duty done and told yeah it's good, go ahead to the hotel

The long story short in my opinion, there is no normal
If you get hotel standby in the am or fbo standby in am, if you are allowed to go to the hotel or have to wait a few hours at the fbo is very dependent on the schedule and who is scheduling
Is it extremely busy, is it busy in the region you are in

It also seems some scheduler's are more confident in their decision making and willing to standby their decision to leave or send a crew to the hotel
Other scheduler's seems gun shy and afraid that they will have to answer to way they couldn't recovery a trip fast enough because a crew was at the hotel with a 90 minute call to wheels up

Take away...There is no written rule on what they do or don't do
Today it is one thing, tomorrow it is another. Hotel reaerve, fbo reserve, go to the hotel, no don't go

What you get, what they give you, and what they want you to do changes daily