Why is HCl used in hydrolysis of sucrose?
The mechanism really isn't much more complicated than what you describe.

The $\ce{H+}$ binds to the acetal linkage. Water then binds to the fructose ring, breaking its bond with the acetal linking $\ce{O}$. Finally, the water molecule on the fructose loses a proton, restoring the catalyst. As Jan mentioned in the comments, the specific acid used is irrelevant so long as it is strong enough to sufficiently acidify the solution.
(Credit to Khan Academy for the image)