Couple things here.

The world of Hydaelyn is made up of three separate, major continents: Aldenard to the West (in which the realm of Eorzea is present), Ilsabard to the North (where the Garlean Empire originates from), and Othard to the East.

It's believed that, at some point during the Fifth Umbral Era in which the entire world was subjected to a deep freeze not unlike a major ice age, the oceans between Aldenard and Ilsabard were frozen solid, thus allowing Miqo'te tribes situated on the southern edge of Ilsabard to migrate over to Aldenard. However, it's stated in the Encyclopaedia Eorzea that those Miqo'te were descendants of Miqo'te that once lived in Eorzea, but were driven out and exiled by the Allagan Empire during the Third Astral Era. While I know nothing beyond that much, we can at least determine that Miqo'te do not, technically, originate from Ilsabard.