I mean it’s the Viltrumite Empire, their range of control is massive, and as we see with the Coalition of Planets they have spies across the galaxy. The Thraxans are a spacefaring civilization, so it stands to reason that some trader or explorer or whatnot mentioned the super powerful mustachioed menace on another planet and word eventually got back to the Viltrumites

No but I assume they make a perimeter around Earth taking into account the average speed a viltrumite can reach and the time they can hold their breath,every planet with a breathable atmosphere resets the count and every planet with inteligent life in the perimeter is target for a search.

Iirc there are only so many planets with breathable atmospheres in the rough (flyable) vicinity of earth. If these planets are known to the viltrumites they could have deduced his location that way.