the relay is getting the main power directly from the 12+ volt battery post. the wire he needs is just a 12 volt switched source which is why its ok. you arent taking anything away from the DME, there is no feedback going back to the DME to be worried about. plenty of people do it this way and there are no freak accidents with DMEs exploding because someone tapped into a ignition source wire for just a trigger wire. Alternator systems generate 13-14 volts when running so there is more than enough power to switch a relay thats already getting power directly from the source.
Also im pretty sure that even with out the AEs triggering off the yellow wire/red stripe in the DME area.. turning the car off, the DME fan/system stays running after ignition anyways, the AE setup picking up a 12 volt signal just as a trigger doesnt do anything to keep it on as the relay only works on way in that aspect. it gets the signal from the switch wire and sends it to the relay but the relay doesnt send feedback to that switched source keeping power to it.