In saponification, base is not a catalyst... it is a reactant. The reaction mechanism has the OH- from NaOH adding to the ester carbonyl carbon forming the tetrahederal intermediate. The next step is loss of alkoxide (!) followed by the neutralization with whatever acid is closest (either HOH or the nascent acid) but certainly the alkoxide eventually rearranges with something to form the alcohol. You see, it is actually the leaving group alkoxide that deprotonates the product acid. This of course supposes that the reaction occurs in the absence of water. In the presence of water, it is likely that water itself quenches the alkoxide leaving group, reforming an equivalent of OH- which then deprotonates the nascent acid.
Either way, sodium hydroxide reacts on a one-to-one ratio with the ester functionality.
It is called hydrolysis because the net effect of the reaction is the addition of water across the ester bond. That said, in base hydrolysis, one of the hydrogens of the 'added water' is actually the sodium ion unless the reaction's products have been neutralized to reform the acid from the sodium salt.
