I foresee two technical reasons acid is used. First, the principle of elimination of the weakest base from a tetrahedral intermediate should rule. If water were to add, the intermediate would possess two alkyl groups, an OH, and an NH2 (after abstraction of a proton from water which generates hydroxide). As leaving groups, HO(-) is the weakest base and thus the best leaving group. This will regenerate the imine (after deprotonation by hydroxide).
This principle similarly applies to hydrolysis of amides. Addition of hydroxide to an amide (and protonation-deprotonation), gives a tetrahedral intermediate with an NH2, an OH, an O(-), and a carbon. Hydroxide is the weakest base so the hydrolysis fails. If the base concentration is sufficiently high, then a second deprotonation of the intermediate can occur to give a doubly charged intermediate. Now, NH2(-) is the weakest base, and a carboxylate is formed.
The second reason is hydroxides of magnesium are milky and difficult to work with. Acidification gives a soluble magnesium salt.