I'm not sure about the source, but as far as I understand, it has been silently retconned that all Minmatar were not caught by the Amarr. The timeline mentioned that on the Day of Darkness the Amarr conquered only Matar and for some unknown reason left other planets and systems alone. It is worth to remember that despite unable to bridge the gap into new systems, the Matari were very advanced before the Amarr came - they even had achieved a global state before the Amarr had conquered the whole of Athra.
I do dislike the current revision of the Day of Darkness, but the spirit makes sense - that the Amarr conquered only the main settlements of the Minmatar, and while they were taking over the rest, the Minmatar managed to capture, reverse engineer or invent a working warp drive. This means that while most were eventually enslaved, some Minmatar managed to struggle on the outskirts of civilization. Where "some" reads "millions", considering the scale of EVE. The Amarr took over them as they went, and the Minmatar were likely pushing deeper and deeper into cosmos - most colonized planets, though this may have also given birth to the Thukker way of life. This is likely made more possible by the fact that, in my opinion, Amarr fleets were likely built mainly to support capturing worlds and supporting ground warfare, not to hold space superiority (and thus, the Minmatar could keep a guerrilla running in hard-to-reach colonies as their blockade runners could outrun the Amarr). The Amarr answer, at first, was cruisers. Only later they started making frigates (with the Impairor being one of the first tries of a "modern" small spaceship).
As a conclusion, while the majority of the Minmatar were ruled either directly by the Amarr or by Nefantar collaborators, some were never slaves. It may be that some "peaceful" worlds with light Amarr presence even had clandestine dealings with the rebels. However, this would have been rare, as while there may have been millions of rebels at any given time, there were billions of enslaved or collaborating Minmatar, and thus the effect of the Minmatar resistance was minimal - until they made contact with the Gallente Federation.