Hi when you are calculating the route the Tesla GPS live location is being pull form the vehicle and it is correct. Once you hit the button to start the navigation the starting point changes to a different one "OLD" location. Then when running the application on the tesla browser the GPS location is not being updated to the current location but stays with the "old" GPS location.
In driving mode (navigation) ABRP will only use the GPS location of the device itself instead of relying on the Tesla reported location (which updates less frequently). It seems like you run ABRP on a web browser - does it have GPS?