Your cold start lever is not connected to your idle speed, rather it is an injection timing advance. You probably won't notice too much of a difference with it in or out. Sometimes, for me, on a cold engine, driveability was a little better with the lever pulled out (less stumbling and hesitation). Now that I have a Giles pump (with advanced dynamic timing) there seems to be no difference.
The cold start fast idle on your car is vacuum activated, so it takes a couple of seconds after you start the engine for the vacuum pump to develop some vacuum, at which point the diaphragm will move the lever on the fuel pump, and your idle speed will increase. After the engine is warm, or a certain amount of time has passed, the switch (located in the fenderwell behind the battery in my car) will turn off and your idle speed will drop to normal. It is not connected at all to the timing advance lever on the dashboard.
So it sounds as if everything is working correctly in your car. You could always get someone local to just visually check your setup. Half of the mechanics I have had work on my car just screw things up, leave the vacuum lines unconnected, don't have any idea how it works or what kind of mess they are making... so I wouldn't necessarily trust a professional mechanic...
P.S. Posting your location helps people respond, or offer to help