This might not be a problem with SAI, but a problem with drivers. If you have both Wacom and Huion drivers installed on your computer, they cancel each other out and mess with each other unfortunately. I have a Huion Kamvas and a Wacom Intuos Pro, and without uninstalling one of the drivers, neither work at all with SAI, SAI2, Clip Studio Paint, or OpenCanvas - a few other people I've seen online have had the same issue and come to the same conclusion.
Sadly there isn't a solution right now other than having to uninstall and reinstall drivers whenever switching tablet, but... hopefully someday the drivers for each once mess with each other.