Well for all we know, the Garleans only conquered Doma - the Japan analogue, not Othard itself. Othard is stated to be a massive region, and with the Primals to deal with and aether-rich Eorzea ripe for conquest, I doubt they're putting forth the effort to subjugate all of Othard.

Once you ping DRK 58 and do the quest, Sidurgu tells you that he came to Ishgard as a boy and his parents were executed in front of him and he was saved by his and Fray's master at the last moment (leading him down the path of the Dark Knight). Pending further information at 60 (which I'm still a level away from), nothing about how or why they came to Ishgard has been detailed.