on time vs to the minute

on time

adj

  • Punctual or according to schedule. 

prep

  • By installments, payments over a period of time. 

  • By a player's running out of time. 

  • Punctually or according to the schedule. 

to the minute

adv

  • Precisely timed. 

How often have the words on time and to the minute occurred in a corpus of books? (source: Google Ngram Viewer )