Hello,
To clarify this from the TDS Sim Software side of things.
Whenever the GPS/VLOC switch is in VLOC position, as in when flying an ILS approach, it is the MSFS autopilot system/logic which takes over. The TDS GTNXi Pro does not handle any logic or handles anything. The TDS GTNXi Pro full follows the official MSFS SDK in terms of autopilot/logic.
Fine tuning of ILS capture is performed via the aircraft's config files, the TDS GTNXi does not have access to these files.
From the TDS side, we are working on a custom autopilot, as a courtesy to our customers, but this is a very laborious process. Not to worry, we have the best intention to our users to continually improve the TDS GTNXi Pro!