Something something 'light cone.' If the machine was turned on a million years ago in another star system and then brought to Earth, the Primer model would put you in the other star system when you climb out of the machine. And then you'd need to make your way back to Earth. (It's unclear to me whether you would continue aging while sitting in the box and waiting for a million years to go by in reverse... But I assume you would.)

So I think the 'other civilization' thing only works if they're already approximately here with a running machine.