Just as I expected, India Post fraked up my order. But Amazon's efficient CC saved the day, so to speak. I contacted them yesterday evening around 7 pm and asked them if they could contact IPS and make sure that my parcel gets delivered by today afternoon. They told me that they don't have a facility to call IPS, and they can only email them. And so they did, apparently. This morning I received SMS saying my product has been delivered. So I checked the tracking status, and according to that, IPS had already delivered my product around 5 pm yesterday! 2 hours before I contacted Amazon! So either they delivered it to wrong person or it was a false status update. I simply got fed up at this point and asked Amazon to cancel the order and they issued a refund within 90 minutes.
I really hope this doesn't repeat in the future. They've assured me again and again that it won't, but one of them said that the couriers for the orders are assigned randomly, so even if I choose Fulfilled by Amazon, there's no guarantee that ATS will handle it. Which is kind of discouraging, I said to them.