I have seen now how when I just kill a rare the silverdragon icon for the rare pops up. I have also rushed to a rare using my fast toy mount to get there very fast only to see it is already dead. There is no way that players could kill the rare that fast. Can you update your addon to warn when the rare becomes available and not when it dies??

It currently alerts you when it first sees a sign of the rare, with the popup appearing when you're out of combat. (That's a Blizzard restriction: you can't create clickable frames in-combat. I've considered making a non-clickable frame when you're in-combat, but that's potentially quite confusing...)

A likely thing that happened to you is that the ⭐ appeared on the minimap as you got closer to it, or maybe while you were in combat, and other players were already fighting it by the time it was able to alert you.

A lot of times I started the fight with the rare and no rare icon pops up. The moment I killed the rare then suddenly the rare pop up for that rare pops up.