Not that culture, not at all. Even nowadays, you get things telling children that they should wash their hands for the length of time it take to sing "Happy Birthday", and a culture less number obsessed -- and without clocks -- would do likewise. Medieval recipes prescribe lengths of time equal to a Pater Noster, or a Miserere, or more than one at need.
Then, time is a funny thing to deal with. You shouldn't have your characters use minutes in a pseudo-ancient world. Most characters in a pseudo-medieval wouldn't, either. Minutes as a measure of time spring from medieval clocks that could mark them. And the tech did not spread quickly. Most characters would still go by the hours peeled out by church bells.
Seconds, of course, are right out. Then I generally have the characters says "Just a moment" instead of "Just a second" to convey that.