Planemad:
You CAN use either oil based or water based paints over either oil based or water based primers.
HOWEVER, the reason why oil based primers have better adhesion to wood is that the size of the alkyd resins found in oil based primers is very much smaller than the size of polyvinyl acetate or polymethyl methacrylate resins found in water based primers.
As a result of this tremendous difference in size, oil based primers penetrate some tiny distance into wood, and this penetration results in better adhesion of oil based primers to wood than water based primers.
The very best adhesion to wood is obtained with drying oil based primers, such as a primer that's made from boiled linseed oil. In that case, the primer consists of linseed oil molecules which are very much smaller still than alkyd resins, and penetrate comensurately deeper than alkyd resins, for still better adhesion to wood.
Water based primer or paint resins are HUGE compared to even alkyd resins that they don't penetrate AT ALL into the wood. As a result, water based primers and paints are more easily scraped cleanly off of wood. They rely entirely on the adhesion of the resin to any surface (not just wood) for adhesion, whereas alkyd resins adhere better because they penetrate into the wood and "root" themselves inside of it.
You don't need to know the rest:
In fact, one of the reasons why you thin alkyd paints with mineral spirits and linseed oil based paints with turpentine arises because of the relative size of alkyd resins versus linseed oil molecules. Since linseed oil molecules are much smaller, they have to potential to penetrate deeper into wood. Turpentine dries slower than mineral spirits, so thinning linseed oil based primers and paints allows more time for this penetration to occur.
By contrast, alkyd resins are too large to penetrate deeply into wood, and so there's no point in thinning alkyd primer with turpentine. You'd get a primer that took longer to dry, but didn't penetrate any deeper. So, it would take longer to dry, but you wouldn't get the benefit of any deeper penetration and therefore better adhesion. (THere are other reasons why drying oil based coatings are thinned with turpentine as well.)