Assuming rational actors I have been wondering about this whole incident:
I am assuming some part of the submarine's mission is probing our defenses. In that case we shouldn't publicly disclose when and when we didnt detect them. Perhaps we have detected them way more than 3 times and choose to do a release on some detection for other reasons.
That is ISPR is letting IN know of the detection because it sees a deterrence value in our detection setup (whatever that is).
Why did ISPR do a press release on the detection? If our goal was only getting signatures of their submarines, the press release doesn't help. In that case we should have let the IN come and go with relative ease while recording their signatures. No need to possibly scare them away by saying we see you.
I believe we do not want IN subs roaming around in our waters. I suspect they may be here mapping the waters/seafloor, which is what we want to prevent.
So through that possibly flawed exercise in logic I can reverse engineer the situation.
1. IN subs have the mission of probing our defenses and mapping the waters/seafloor.
2. PN has detected IN several times more than what is said in the ISPR press release. This is because it makes sense for the PN to not reveal all their detection ability.
3. Doing the press release on saying we detected you thrice says we can detect you sometimes so please stay away and stop mapping our sea floor. So that the Indians don't know the full extent of our detection capabilities (trying to fail the IN probing mission) and
deterring future missions (trying to fail the IN mapping mission).
But then I know very little of naval, let alone submarine, peacetime operations and warfare so I am just trying to think of interesting background to the whole incident