It could be the last remnants of the spilled fuel, just getting shaken out of wherever it had pooled, although I'd be surprised that it hadn't evaporated.
Don't worry too much about the engine being on with a leak, a lot of design goes into stopping the fuel igniting when they don't want it to. The fuel tank is at one end of the car, the engine is at the other.
I knew someone whose bike (which have their fuel tanks above the engine) had a leak, and it was dripping on to the engine and fizzing as it instantly boiled - no fire.
I filled up a few weeks ago so must have been driving around with the petrol cap like that for a while...I noticed a smell of petrol a last week but I didn't realise it was my car.
DH noticed the smell today and looked underneath it and saw it dripping. He tightened the cap but it began dripping again when he turned the engine on. And now I understand it is dangerous to turn the engine on if there is a leak...
How big is the leak? Is it gushing forth, or just the occasional drip? Is it coming from the front of the car or the rear? Are you at home or out on the road?
They could probably leave the car in dealer's car park so it's leaking on their tarmac rather than yours, however you're going to have to sort your transport to and from the dealer. If you're at home, just leave it until tomorrow.
Have you had an accident recently? Petrol tanks are pretty robust.