Ramsay So why do so many things show below the horizon and other things that are below the horizon the scope will rotate to?
There are two possibilities that I can think of. One is that the the hemisphere (north or south) is in error, but you would have already noticed that.
The other is that the ASIAIR is not getting the correct hour angle (angle of the RA motor axis relative to the Meridian) from the mount. Mounts that do not have encoders (either an absolute encoder, or a relative encoder with an index position), require a star alignment to know the precise Hour Angle.
With mounts like the Takahashi, there is a Zenith Alignment method for daytime Solar use (plumb the OTA pointed straight up and align the software relative to that position).
Check with your mount's manual what they recommend with aligning the mount before you start during the daytime.
If there is no such information, you might try this (it might get you close enough):
0) to prepare things, level your mount in the east-west direction (crucial), and point your RA axis at least within a couple of degrees of True North (not the Magnetic North). There are many tricks to find True North in the daytime (just recall the tricks from your Boy Scout days). The best thing is to polar align the night before, and leave the tripod where is was.
1) disconnect (green slide switch) the mount from the ASIAIR in the Telescope Settings window.
2) move your mount to the home position (with many mounts, it is declination +/-90º (- if you are in the southern hemisphere), and with the counterweight shaft pointed towards ground.
3) power off the mount, wait a couple of seconds and power it back on again.
4) re-connect the mount back to ASIAIR in the Telescope Settings window.
At this point, check the Right Ascension in ASIAIR's Telescope Settings window. Does this agree with the RA in your Hand controller? You may need to select a different window in ASIAIR and choose the Telescope Settings window again to get ASIAIR to refresh the information (the ASIAIR GUI is a mess -- some items are auto refreshed, some are not, all within the same configuration window).
If the RA is way off, then ASIAIR is clueless about where the RA axis motor is pointed.
With mounts that have no encoders (either absolute or relative encoders -- I think your mount counts as one of them; I have never used a Celestron mount in my almost 60 years in the hobby, so I don't know), ASIAIR will require you to star align the mount before it can connect to the mount. Just do a fake star alignment on your hand controller, confirming the position of each star it is selected by the mount, as if you had actually centered the star in your eyepiece before confirming. Home the mount with the hand controller before connecting to ASIAIR.