That's correct, and although I don't have the book to hand to confirm, I think it was at least a couple of years before Gyr Abania was secure and Gaius set sights on Silvertear Lake.
Edit: I've cross-checked. Conquest of Ala Mhigo is 1557, and the Battle of Silvertear Skies is 1562. A whole 5 years of consolidation.