I'd defininetly check out the condition of your rear suspension bushings and your alignment. Also, are there any weird extremes between the front and rear of the car (tire pressure, spring rates, etc.)?
A couple of different impressions. ... I've never owned an e30, but had a 318ti with H&R race springs and Bilstein sports. That created a noticeable amount of toe-in at the rear of the car, but the car never experienced snap oversteer. It was actually quite nice because, despite not being a powerful car, you could put your foot in it to bring the back end out -- and control it with throttle to an extent -- or you could drive it like a front wheel drive car (trail brake) to lighten the rear (this actually worked quite well in the rain since it was too slick to get back into the throttle early).
My 2002 is different. (Bilstein HD/Eibach Sport/ 22/19 mm sway bars/ rebuilt subrames with urethane everywhere). Even after all that suspension work, it is still typical 2002 in that it has a moderate amount of understeer and gives only a hint before transition to oversteer. At that point, the back end will kick out a bit before regaining traction. When you're not used to it, it's weird at first.
FWIW, both of these cars have similar rear trailing arm suspension to your e30.
When I bought a Miata, inducing oversteer was much less forgiving. With its short wheel base, the transition to oversteer is more sudden. I've also autocrossed my friend's MR2 Spyder and it is a true mid engine car, complete with snap oversteer (these are great cars, btw).