Should you let PVC primer (purple) dry before applying cement or is it okay to apply cement over wet primer?
No - PVC Primer does not need to 'dry' before use - in fact, it needs to be wet to do it's job and not impede the cement - remember, plumbers in a hurry use this daily and aren't sitting around waiting for the primer to dry before grabbing the cement.
I make sure everything fits first, then grab the primer and swab it on, set it down and grab the cement and swab it on. If you wait - it's likely no more the 10 seconds. If you've waited a few minutes because you've gotten distracted, made a mistake or something and it's fully dry, just reprime to be sure the plastic is accessible and softened for the cement. If you don't- it can prevent the cement from bonding as well to the plastic.
The cure-times listed on the can are for after the cement cures- typically 2 sets of times will be listed - one for handling and one for pressure testing.
The primer needs time to do its work. In the summer time I wait for it to be dry. In systems that are using higher pressure or cold weather I really do wait several minutes. The instructions do provide times for size and temps but my can is not readable. I have only had 4” at 90 psi fail but after that I did start waiting longer after reading all the instructions. I think there is some safety built into the suggested times.