There's NO distributor on a '93 Sunbird, therefore NO Cap and Rotor.
The other things mentioned by bandit_60 are good to check/replace yet not the sole cause of WHY such is happening.
MANY PROBLEMS WITH IDLE can be traced to Vacuum Leaks, as stated in a Haynes Repair Manual.
Start by tracing ALL Vacuum Lines and replacing with new. Even though Vacuum Lines may LOOK good, they can be faulty.
May very well solve the problem.
WHEN was the last time a regular maintenance service was performed on Transmission? New Filter and Gasket, some new Fluid??
WHEN such is done, inspect the Magnet in the Pan for excessive Particles before cleaning and reinstalling.
There might be some blockage for the Trans Fluid at the Radiator which could well cause hesitation.
A Haynes Manual (available at autozone, advance auto, o'reilly's, etc.) specific to that year will indicate Sensor locations though I know not of one for the Trans.
NO Engine should race up "a few hundred RPMs" just from changing gears. (Our '64 Chevelle increases Idle a bit when going from Gear to Neutral but not very much)
THAT seems like an Idle adjust issue or possibly the Idle Air Control Solenoid/Sensor on the upper Throttle Body which costs $62.00, or the Throttle Position Sensor which ain't cheap either.
MY '93 Sunbird LE (2.0, Auto.) does NOT idle up much when I go from Gear to Neutral, nor does it drop much from Neutral to Gear.
I recently replaced the I.A.C., T.P.S., E.G.R. Vacuum Solenoid, ALL Vacuum Lines, Plugs, Wires, Oil, Filter, Trans maintenance, New Timing Belt and Water Pump, Thermostat, and after all these, still had idling problems which, after a shop diagnosis, discovered the problem was the Head Gasket.
I'm waiting for the shop to finish and it ought to run well for many years after all these upgrades.