I don't think it was intended this way by the movie writers, but there is a historical sequence which could explain it:
1936: Olympic broadcast leaves Earth at speed of light. Received by aliens at Vega 26 years later -- 1962.
Aliens see teevee broadcast and think, "hmmmm. These brings have invented teevee. The first broadcast is of a military leader appearing in front of a roaring crowd. Better keep an eye on them."
1945: Three atomic bombs are detonated in a 30 day time span on Earth. The aliens might well have devices capable of detecting atomic blasts at stellar distances. They see the atomic blast evidence in 1971 (1945 plus 26 years),
Aliens say, "uh oh, these guys have invented nuclear weapons. Maybe we better have a little talk with them ASAP."
Aliens broadcast The Message to Earth shortly thereafter. It arrives on Earth in 1997 -- 1971 plus 26 years.
Makes good sense time wise albeit not about the "let's have a little talk with them ASAP" because that did not happen.
What if they sent someone back with her through the wormhole which connected back in time to Earth 18 hour ago?
They did. That's why there are a lot of Vegans on Earth these days.