If you're standing perfectly still, then eventually, the tachyon will reach you in less time than it would take for light to get there. You wouldn't be able to see the tachyon coming until it already passed you, which is still no big deal. If you had a telescope pointed at me, you would receive the tachyon before seeing the image of me pressing the button to send it. Curious, but still no huge problem.

The issue comes if you start moving. In relativity, from your perspective, you are standing still while Earth appears to be receding. This introduces time dilation: From your perspective, everything in the universe — including the action of me pressing the button —​​ slows down. In fact, if you're traveling fast enough, you could receive my tachyon and send a reply before I even hit the button in the first place; you can send a signal back in time.