My experience with inverted spins is a bit counter to what happened to you -- although it's limited to the Citabria/Decathlon series. When inverted (with an inverted -- negative g -- entry), I've found that it actually takes pro-spin input just to keep them IN the spin - that the vertical stab hanging in the wind is stabilizing enough on its own, and you've actually got to take pro-spin action to mitigate that.
But that's with pretty much a standard (but inverted) entry. After spinning a lot of different airplanes and gliders (all aerobatic, except for some 150's), sometimes entering from a botched acro manuever, I've found that every once in a while an airplane will surprise you. (I'll put in the standard here: "what MTV said") Especially when you're entering outside the norm. And the first bit - sometimes a 1/2 turn, sometimes 3 or more, can be really goofey sometimes.
Usually, after some number of turns, things stabilize. Bad news is, sometimes they stabilize in a bad way - making recovery tough (if doable at all). Most I ever did was 12 turns, it stabilized out real nice after about 1 1/2 turns. But that was in a blanik L-13 (glider), a tough, forgiving, and sweet old bird, and entered from 12,000 ft. Gave up 4000' with the spin.
--Tony
Besides, always know which way your aeroplane is pointed.