I'm having the same difficulty and I don't think it's user error. In the campaign, the very moment that manual reversion is switched on, the ailerons begin moving back and forth in full deflection each way, oscillating several times per second. This is completely independent of any joystick control. With no user input, the plane rolls left then right uncontrollably. It flies as though a toddler were playing and moving the stick back and forth as fast as they can, trying to break your expensive joystick in the process.
The Recon Stewart youtube video provided as an example how to do this correctly has an excellent discussion in the comments section about this problem which seems to have started after the 2.5 beta update. There is also a video posted here:
which is the same behavior I have been experiencing. External view of the plane shows the ailerons rapidly cycling through full deflections right and left.
Another thread here stated that someone found a workaround by changing the loadout at the beginning of the mission to something not empty and making sure not to jettison the stores when the instructor tells you to. For some reason this fixes the flight model and prevents this from happening. I have not yet tried this to confirm but I'll try to do so and report back.
Update: Yes, I was finally able to pass the mission by changing my loadout and not jettisoning the loadout when the instructor says. With that done, the manual reversion landing was controllable and there were no aileron oscillations. I think the fact that this worked seems to rule out any issues in my control bindings or incorrect user control. Does seem to be a bug having to do somehow with a clean loadout.