In fairness, it hasn't always been like that everywhere. In my hometown, the move to 'prepay when using cash' only happened about 10 years ago. I distinctly remember working at a gas station in high school and dealing with older customer who refused to believe that they couldn't just pump then pay.

Agreed, and I'll go one further saying that it's still not 100% this way everywhere. I'm from a pretty rural area and at several of the stations there you're still free to pump then pay in cash.

I actually didn't realize pay-first for cash transactions had become the standard until recently as I made the swap shortly after 'pay at the pump' became common and never really looked back. How does it work? You just estimate how much you need, and the pump cuts off at that point? If you can't hold that much you go back for a refund?

Yes, if you overpay then you go back in and get the change back. If I give the cashier a twenty, but only pump $10 worth, then I get $10 back from them. Most people are pretty good at estimating it though, so generally the people that pay in cash will just leave the few dozen cents they didn't use.

This is the first time I'm hearing about petrol stations where you pay cash in advance and I live in EU. Just fill up the tank and pay at the till?

No, pay at the till, then fill up the tank. This is in the US.