In Carl Sagan's Contact, we were only able to determine the signal came from the star Vega because it was the only star that would have been at the right distance to receive our earliest radio signal and transmit it back to us - also Vega is relatively close by compared to other stars, close enough that our parallax created by our orbit around Sol was sufficient to get a read on signal source.

A deliberate attempt at active signaling would remove all doubt for an extrasolar observer.

Liu Cixin's The Dark Forest explores this scenario in depth. I would explain more but don't want to reveal some important spoilers.