What more than likely happened is that an electrical leak developed as a result of the ballast heating up as it continued to run, eventually faulting and popping the GFI.
Anyway, back to Gmann, yeah, a GFI that is tripping through SOLE VIRTUE of overcurrent is definitely not acting properly. They just aren't circuit breakers or otherwise an overcurrent device. While I won't argue happy's claim that it happened, I would argue that his claim constitutes normal operation of a GFI.
When I say sole virtue, it's also important to remember that GFIs do exhibit variations in sensititivy. UL defines the maximum current and response time that they have, but some are way more sensitive than they need to be, which can also cause them to nuisance trip. A certain amount of leakage current is not uncommon in electronic devices, so sometimes a lighting system may trip one GFI but not another. The fact that the OP tried two different GFIs excluded that possibility out of the gate so I never brought it up.