I cross often by car in Famagusta. This is the drill at that crossing:
Drive up to the Turkish immigration booths and show passports (for a scan) and car insurance (there is no interaction with ROC immigration at this point).
Have fun in the North.
On return, stop at Turkish immigation booth, show passports (for a scan).
Drive about 50 feet and show passports to ROC immigration - half the time they just wave you through; other times they look at the passports and ask you what you have bought and maybe look in your car. There is no scanning of passports by ROC immigration. They seem to be looking at passports more often these days because of migration issues. Fair enough.
Then go about your business in the ROC.

My interactions have always been pleasant.

BTW, I am an American and am usually travelling with Brits. People of other nationalities may have a different experience though all the crossings I have witnessed appear to be the same as my experiences.