"Required time" is a little vague, so I will not use those terms. I assume that you are traveling to a train station, not necessarily by train, to catch a train, for example.
According to schedule; punctual or punctually.
I assume this is your schedule (it does not have to be). So, if you planned to arrive at the station at 9 am, and you arrived at 9, then you would be on time. The implication is that you planned to arrive at the station before your train departed.
Before a time limit expires, early enough
There is generally an implied "for" or "event" when using in time.
So, for example,
- We reached the station in time to catch the train.
- We reached the station in time for check-in.
So for example, you plan to arrive at the station by 9am to catch the 11am train. The traffic was awful, but you finally arrived at 10:30am and barely caught the 11am train. You were not on time (with respect to you schedule) but you were in time to catch the train.
I believe this is a matter of idiomatic use and not so much grammar. The difference has also been discussed on ELU: “In time” versus “on time”.