Don't confuse "on time" and "in time"

on time

If something happens punctualpünktlich, termingerechton time, it happens at the time it is supposed to happen. In other words, it happens punctualpünktlich, termingerechtpunctually:

Example: My flight to Munich was on time last night. — Mein Flug nach München war gestern Abend pünktlich.

We can emphasize that something began punctually by adding the words “right”, “dead” or “bang”:

Examples: The concert started bang/dead on time.  — Das Konzert begann absolut pünktlich / auf die Minute genau.
You’re not late; you’re right on time! — Du kommst nicht zu spät; du bist ganz pünktlich / du kommst genau zur richtigen Zeit.

in time

If something happens in timerechtzeitigin time, it happens early enough for you to do something else:

Example: Because of the heavy traffic, I didn’t arrive at the station in time for my train. — Wegen des starken Verkehrs kam ich nicht rechtzeitig für meinen Zug am Bahnhof an.

This is why we talk about “just-in-time delivery” in industry. The parts are delivered just before they are needed for assembly.