Tesla Autopilot, aka Tesla Adaptive Cruise Control (TACC) will not use the traffic signs or GPS mapping data to adjust your speed. If you have purchased Full Self Driving (FSD) then I believe the Tesla vehicle will moderate the speed based on the signage and the GPS mapping data.
You adjust the speed while Autopilot is engaged by rotating the right thumb wheel up or down. To change your speed in 5 MPH increments you can flick the thumb wheel up or down. (That's what I do when entering a different speed zone.)
Example 1: If I am driving with Autopilot engaged at 39 MPH and flick the right scroll wheel down the Autopilot speed will change to 35 MPH. If I flick the thumb wheel a second time the speed will change to 30 MPH. The other thing you can do is disengage Autopilot and when you exit the speed zone, i.e. a school zone, when you see the Tesla display the current speed limit on the screen (this is either from reading a sign or from the GPS data), then I re-engage Autopilot.
Example 2: If traveling on a road with a 30 MPH speed limit and making a turn I disengage Autopilot. After making the turn the Tesla displays the previous speed limit (30 MPH) for perhaps 100 yards before updating to the speed limit for the current road (35 MPH). I wait to re-engage Autopilot until the Tesla screen acknowledges that the speed limit is 35 MPH.