Yes this is correct. It only reports its position infrequently and mainly on engine off. The only way of doing what you are thinking (without a phone), is to buy a cheap GPS telematics unit and wire into the 12V power socket in the boot (assuming you have it). It is pretty cheap to do and ensures that it is not powered when the engine is off.
The other way I have achieved this is (again as always with HA - depending on your router), you can detect when your phone connects to home Wifi. Mine generally does this on the drive and most times triggers the action quickly (but not always). I use this to turn the outside lights on if it is dark when arriving home. Normally on by the time I get out of the car - but maybe I mess about a lot!