Your Hicas most likely wouldnt cause what your talking about.
Some factors we must know before I could even begin to give you a decent answer.
1- how sharp was the corner,degrees would be nice?
2- how fast were you going when you entered the corner?
3- how fast were you going when it started to oversteer?
4- was the road wet, dry, or dirty?
5- when was the last time you had a 4-wheel alignment?
These are some rather important factors to take in.
Lets say its a 120deg turn with a posted limit of 30MPH this means it would be a realatively sharp turn, I found that my stock suspension 300ZX can take most corners at 2 time the posted limit, NOTE: I said MOST.
Now if you went into the corner carring to much speed the front end will begin to lose grip and "push" into the corner, causing a sort of shudder affect through the steering wheel. If you were carring to much speed after the corner and the rear wheels were pushed too hard then you would most likely had a oversteer problem, this meant that you were probly too agressive on the throttle at the point of the turn, this would lead to a great begining to a "power over" drift technic, but not good if tring to go fast. This can be further inhanced by haveing too much or too little rear camber.
My solution to this problem would be get a four wheel alignment done, then take your car to a open lot with NO, I repeat, NO other traffic or cars, and very little things you could hit that could damage you or your car. Then try and do a few donuts till you learn how to control the AoA of your car. (AoA means angle of attack, or where you are pointing the nose in relation to where you are going.)
My last couple of tips would be get better tires.
lastly, When you are drifting, "fishtailing", powersliding, or what have you, the car WILL go where the steering wheel is pointed, so if you over correct the car will whip back the other direction where the front tires are pointed, fast but persice movements will keep a car under control in a oversteer situation. I learned on the mountain roads of WV in a 89 Ford Ranger, and more in the military with the highspeed pursuit and evasion classes I took. You can do alot of funky stuff in a car that looks out of control and yet be in complete control if you stay calm.......
Hitchhikers Guide to the Galaxy "DONT PANIC"