I'm not sure for how long this has happend, but I recently had to change the backup time from 9PM to 1AM on one of our schedules, the backup job just started immediately after I pressed finish.

If you didn't change the DATE at the same time, that's probably what was supposed to happen since 1am occurs way before 9 pm on the same day... especially if the option is checked to run the task if schedule missed as soon as possible.

It shouldn't happen again...

I would call this unexpected behavior, and therefore undesirable.  And fixing this should have no negative effects, because if there are any users who did want a backup to run immediately upon setting a past backup time for the same date that the backup job is modified or created, then they can always manually start a one-off backup after saving their changes.