Dear propus,
Perhaps this screenshot (ASIAIR V1.2 Beta 4) might make it clearer.
http://www.w7ay.net/site/Images/ASIAIR_Plate.PNG
The response from ASIAIR's plate solve was obtained after I had previously asked ASIAIR to choose Polaris ("Choose Object" in ASIAIR's Telescope Settings window), and after that, did a plate solve. In this case, the telescope is pointed at an artificially generated star field of the NCP region that is displayed on a laptop about 10 meters from the telescope. It is completely overcast outside.
Notice that there are three options you can choose after the plate solve: (1) Cancel, (2) Sync & GoTo <star>, and (3) Sync Mount.
I don't remember what the window in the release version showed exactly; the above is a screen capture from the v1.2 4th Beta of ASIAIR (Firmware 2.28).
If you had previously chosen the object in SkySafari instead of from ASIAIR, what you want to do is to choose "Sync Mount" in the ASIAIR Plate Solve result window, then switch to SkySafari and go perform another GOTO in SkySafari.
After the "Sync Mount" from ASIAIR, the three devices, viz, the ASIAIR, the mount, and SkySafari should all be in agreement that the telescope is pointed at the plate solved location. The extra GOTO in SkySafari slews the mount from the plate solved location to the selected star in SkySafari. After that GOTO, all three devices should all be in agreement that the telescope is now pointed at the object that is selected in SkySafari (or very close to it).
If plate solve does not work with SkySafari for you for now (it should; I have used it myself), you can still use SkySafari -- after a SkySafari GOTO, switch to the ASIAIR Main Camera, take an exposure, and you will see the star is probably not fully centered in the main camera's crosshair. Use the RA-DEC directional buttons to center the star manually (you may have to go into the Main Camera's Advanced Settings to ask for "Continuous Preview" so you don't have to manually take an exposure each time you try to center the star). Once the star is centered in the ASIAIR main camera, go back to SkySafari and you will probably notice that the cursor in SkySafari is a little offset from the target star. However, since we know that the star is really centered in the camera, instead of a GOTO in SkySafari, click on "Align" instead. You will notice that SkySafari now moves the cursor on top the selected star without actually moving the mount. At this point, the ASIAIR main camera, the mount and SkySafari are in agreement that you are pointed at the star.
If plate solving for some reason fails to work for you with SkySafari, you can try using ASIAIR's GOTO (I have stopped using SkySafari myself after ZWO added stars to the ASIAIR database). Just go into the ASIAIR Telescope Settings window to Choose Object, and then do a Goto from the Telescope Settings window itself, or do Sync & Goto from the plate solver to get precisely on top of the object.
Clear skies (unfortunately not here NW Oregon :-),
Chen