"у меня" is not a complete phrase and can not be reliably translated without context. But most often it means just "I have". As for Pimsleur logic, I can neither comment it nor recommend.
This is the way automatic translation works. It is always awkward and often unintelligible.
I can guess that original phrase was "У тебя в машине есть бензин?" I'd translate it like "Do you have a gas in your car?" or "Is your car fueled?"