Most likely the former. I've owned an n/a SW20 MR2 for 5 years now, daily driven, and the snap oversteer is there. It's just on the very upper limits of the car, or during very low grip situations if you don't know what you're doing. You more or less have to be over-driving the car to get that kind of reaction out of it. It's probably worse on the turbo though, because it's got a good 150lbs extra or more around the engine for those components and the beefier transmission.
Opinion on MR2 SW20?
Jackson Rivera
Christian White
I had a 1990 sw20 with the na engine and it was a really sweet car. Fast through the corners, reasonably economical and girls liked it. It had electrical problems towards the end which was quite common apparently but i still sold it for good money. The only trick to surviving mr2 ownership is to drive it like a fwd. Very low steering input, smooth throttle input and dont step off the gas suddenly while cornering hard.