Check that throttle cable or Cruise control cable is not holding throttle plate open
Unplug the IAC valve while engine is running, it should close and idle should drop down to 500rpms or engine may even stall, either is correct.
If idle stays high then IAC valve is stuck open.
Remove IAC valve and check it, plugged it in while it is off the intake and turn on the key, IAC valve should open all the way and then close a bit.
"New" no longer means "it works"
New now means "never tested but warrantied", we are now the Quality Control Department for most manufacturers.
IAC valve uses a Step or Stepper Motor, computer sends it a "pulsed voltage", like a Morse Code, the various pulses tell motor to turn to its various "Steps", there are over 100 steps that can be "called on".
Step 20 might turn motor 90deg from 0
Step 40 180deg from 0
ect......
Each Step opens or closes the Valve connected to the motor a specific distance.
The Computer "Learns" which Step causes which RPM level, this is why the mechanic asked if you drove it, it allows the computer to "reLearn" what Steps to use on the new IAC Valve motor, but that can happen by just running the engine, no need to drive it, but it does need to warm up and cool down a few times(drive cycles).
New IAC valve will cause wandering lower RPM at idle as computer fine tunes which step sets what RPM, the above 2,000RPM is something else.
The high RPMs in your case reads like IAC Valve is simply opening all the way when powered up and computer has no control of it
Heads up: if you see what "looks like" and idle adjustment screw on the throttle linkage, don't adjust it, it isn't an idle screw.
Fuel injected engines can't use an idle screw since there are no "jets" like a carb had, the screw is for anti-dieseling and TPS(throttle position sensor) lower voltage adjustment.
If you have a volt meter set it for DC volts, with key on/engine off test voltage on TPS center wire, it should be .69 to .99volt, under 1volt, you can adjust that screw to get correct voltage if it is not in the above range.