Is it 'in time' or 'on time' here?:
...
GERRARD: Hello. Yes, speaking. Sorry I can’t let you have the props in time for rehearsal...
It's from a story in which Gerrard talks over the phone to someone and says a specific time duration, which I infer from this:
GERRARD: ... Well, tell him to phone up directly. I must know ... Yes, I expect I’ll still be here, but you mustn’t count on that ... In about ten minutes’ time. Right-ho. Goodbye.
This is the story where the line is.
From this, can I say that the "in time" here is correct too, or is 'on time' the correct phrase to be used in the sentence? My point is that, since a specific time is mentioned, from so-to-so, 'in time' should be correct. Or, should it be something like "in this time" or "in the time" where 'this' and 'the' refer to the time interval?
If I'm not wrong, 'on time' is usually used when the task is completed at the brink of the moment. As the meaning is decided by the author, I only say that it either would be either 'in time' or 'in <pronoun/word referring to the time interval> time' as when such a phrase is used, it usually means/refers to "between (time1 and time2)"/"in the time of (time2-time1)", time1 and time2 (in this case, the then-current time and that + 10 minutes) being mentioned earlier, and its meaning is/can be totally different from on time's.
I know that there are many grammatical errors in the sentences, but the question is the title.
Please correct me if I'm wrong; I hope this makes sense.