The game of cat & mouse has been played in sea's between subs and sub hunters since the development of the submarine.
During the cold war, the US & USSR were actively playing this game.
Submarines are prowlers of the deep, and are designed to remain undetected in order to complete their mission.
We during peace time, continuously conduct ASW exercises with our own subs in every possible scenario. These exercises benefit both the platforms.
Since 1964, PN has been operating submarines and now after 50+ years, we have a well trained submarine force which has proven it's worth in 1971, by sinking an enemy vessel. These doctrines are developed over a long period of time and produces qualified crews who are well conversant with submarine operations.
PN has also been up against its adversary since the start and used the Ghazi in 1965 in an aggressive posture.
Now coming to your specific concern,
Submarines are used in peace time to gather intel, track & monitor shipping lanes/routes, monitor adversaries naval movements, stay hidden in strategic choke points and many more, but they do all this while remain invisible.
As soon as it is detected, it loses all it's initiative and has to go back.
In this case, the sub was detected and localized (which is done while it is submerged and not on PD).
Then the procedure is adopted to let the sub know, that is has been localized & identified and is forced to come to PD or surface.
The video which was released was made by the IR camera, after the sub came to PD.
If they were defecting, then they would have made it obvious just by giving a call on the UHF guard frequency, and we would have guided it to our nearest port. So it's not the case.
We over the years, have tracked and have a pretty clear understanding of how our enemy operates, the area where they operate and the depths they operate.
This is not the first time, we have localized our enemy sub, it has been done so many times in the past. I myself have tracked one of their subs during one of our exercises many years ago.
This is the first time the IN is operating french submarines, and were probably testing it's capability and limits.
PN will and is looking into this matter deeply and from all angles, as it is a matter of survival.
Rest assured, we have our eyes & ears open.