I’m currently using Vallejo white primer on my models. I know that thinning one’s paints is a popular idea, but should I thin my primer too?
No, primer is not designed to be thinned. On the other hand you need to apply it in thin coats so it doesn't clog details. The Vallejo primers should work rather well with that. Remember that the objective of the primer is to become a good surface for the actual paint to stick in. If it's formulated to also serve as a base coat like the Army Painter sprays, then good, but most don't. They're just part of the preparation.
If you're using the P-U primers, they are pretty forgiving when you go heavy with them. Their official video explains it much better than I can. EDIT : this one explains it better.
The multiple thin layers with airbrush, from what I read, is more about getting it to stick and keep the proper "texture" than anything else. And instead of thin layers, think of mist layers or dust layers, that is how it looks with the first ones (and that is the name used in automotive field, other would be wet layers). Instead of thinning, play with the needle & tip (if you can change them) and the pressure if it gives problems. And remember there is also flow improver, retarders and other products, not just thinner (and water). If you are talking about hair brush application...
