Personally I don't trust the backup.xml to import and check on my setup.
If you give screenshots of your active profiles and their contexts, and/or Exported Descriptions (long press the profile > tap 3-dot-menu > tap export > clipboard, get that into the message. Exported descriptions of profiles are how Tasker users help each other on this forum, in general.
Did you try the "back" button on Tasker main page? Sometimes Tasker's main page erroneously shows a profile is active when it has been deactivated, especially when the state just changed. Is it actually firing off the Enter and Exit tasks of your Time Profile? (regardless of showing "active" as you suggest).
When I use a Profile action in a task, and tell it to disable some of my profiles, it always works. However, I use a AC-battery status context as the trigger for turning some profiles on and others off, so I am not using Time contexts for that. There could be an issue with Time contexts not being noticed, or triggering for an instant and not turning off or triggering and staying on until terminated another way (as you suggest, "turning Tasker off").
OH. If the time parameter in a context is SET, say 12:00 AM to 12:05 AM, AND the Profile is "active" what that means is the "enabled profile" will be "triggered" or "active" for 12:00 AM to 12:05 AM. I ask this specifically because I suddenly got a clue in your question that you might not be totally clear on what "enabled" / "active" / "turned on" / "triggered" means with respect to Profiles.
Basically, you can turn profiles off (%PENABLED ~ false... I think), then they won't trigger even if the Time or AC state or whatever context is actually happening now.
Or, the profile is enabled, and further, "active" when the context is matched. When activated by the actuality of the context, the Enter task is run. When the context is over (ie. it's 12:06 AM), the Exit task is run.
The time context if a Profile does not have something to do with turning the profile or off, but instead whether to run the task when the context is actual.