They got a follow-up message claiming there were survivors. That message was certainly false and illusory, yes, absolutely. Maybe the follow-up message was not precisely at the same range, but it came soon after and so was still many light-years, requiring a voyage at warp seven to get there before too much time had passed.Well, there's something I've never though of. Was the distress signal legitimate, sent by the Talosians, or an illusion by the Talosians? It seems that the first two possibilities could only be the case at all for the first message, since it would have to have been sent out 18 years ahead of time. The second message was definitely faked, since there was no group of survivors after the crash, and it almost certainly has to be an illusion after realizing Pike didn't take the bait and needed more encouragement, since it seems unlikely the Talosians would realize Vina was half of the solution to all their problems within a few hours of the crash.
The Keeper said they had sent a fake message, in the singular, to bait them, so that would seem to indicate that the first message was legitimate. Apologies for my confusion, but I still believe they were still many light-years away from Talos IV when the illusory message came, more likely more than 18 than less than 18.
The approximate range of the faked message was indicated in the very first scene, but, yes, it's likely the first message was legitimate.