Aircraft is Quoted from Previous Home Base

"All my quotes are still from the old home base, not the home base I just updated it to"

The reason why your aircraft is not being quoted from the new home base is probably because it is still in the old home base in the aircraft's schedule. Avinode is quoting based on the location of your aircraft in your schedule. If this problem occurs, the schedule might not be up to date, or the FMS sync might be off.
To find out where your aircraft is located at a certain time, go to the schedule tab to have a look.

We can only help you change the home base, but we cannot make changes to your schedule data as that could go very wrong since we don't know exactly where your aircraft is at any point in time.

Should you have a manual schedule, this will require you actively move the aircraft to the current position by creating a manual positioning leg.

Should you need any help on how to create an activity in the manual schedule, please have a look at this article: Schedule Manual - Creating new flight activities