In the expression the word time is used outside of its normal context, in that the person is not getting any time information but there is some information, which gives a sense of duration for example. So when a person does something on time he does it within a given period and is not late.
If on the other hand a person does something "in no time at all" or in no time, he does it within a very short period, which is negligible.
Now the learner has to accept that fact that he will be thinking outside the box in that he will be using the preposition ' in' differently from how it is intended to be used classically. If a person has done something " in the nick of time", this means that he has been able to complete a task just before it would have been too late. One can associate an emergency situation in order to use this expression properly.
