To me, Vallejo primers are noticeably more coarse than Tamiya primers. Even when I thin Vallejo primers with distilled water + flow aid, they are still much less fine than Tamiya. Are they supposed to be coarse? Or, do I need to shake the bottles more rigorously before spraying?

I use the Vallejo Airbrush thinner and mix is almost 60% paint to 40% thinner and spray on light coat and is seems fine.

I have to agree. I thin about 50-50 and have had great results.

Aren't Vallejo primers supposed to be sprayed out of the bottle? Thus, I use only a little bit of thinner. Maybe I should thin more.

My 2 cents - I shake it thoroughly and spray it directly from the bottle with absolutely no issues whatsoever. I don't thin it and won't use any other primer now.

The white one does seem a little 'coarser' however sprays and dries fine and the black one goes on very 'wet' and dries smooth!

I haven't used any of the other coloured primers

I as well use nothing but Vallejo primers, and they always go on smooth for me. No thinning necessary.

Possible that yours is drying a bit before hitting the model? This would give it a rougher texture than normal, but haven't experienced that myself, as they usually dry to a satin finish.