Uncle Alvaro was Columbian, and was not at the Alamo. It was kind of confusing because the story had them pitting the two ancestors against each other, and Manny even made a crack about how they were likely to find out that the uncles inevitably killed each other. But point in fact, they were merely being contrasted against each other for their merits as "heroes", and not as enemy combatants in a specific battle.
Speaking of that battle, how was it not a huge tipoff to Jay that his ancestor might not have been the hero he thought, if his uncle's claim to fame was that he "survived the Alamo"?
(There were in fact survivors, but it was non-combatants, such as women and children, Others who had left the Alamo prior to the battle, are also considered survivors. But someone like Jay's uncle, would have absolutely met their demise. Unless of course they went the route that was uncovered on the show. Though in fairness, I really don't know if something like that even happened.)