You seem to think that a stable supply voltage on your sensor will fix a problem.
"The output is sensitive to input voltage"
Maybe the (unknown) sensor has a ratiometric output, in which case it can't be detached from Aref.
If not, and you want a stable output from your device, then you also must provide a stable reference voltage for the A/D, since A/D result depends on both.
The (unknown) Arduino's default Aref could be worse than the output voltage of the (unknown) tilt sensor.
Leo..