How do we check the time when a transaction hits x confirmations? Consider the transaction 948a427.. which has 3341 confirmations as of now:



We can see that the time the relay is received at 8:36:30 and it has one confirmation at 08:50:04 (after 14 minutes).

How do we find out the exact time when it has 3 confirmations?
The first confirmation was in block 298902, so the third confirmation was with block 298904, which is timestamped as 2014-05-03 09:42:49 (66 minutes after it was first received).

However, this timestamp is later than the one in the block after it, suggesting that a timestamp was pretty far off. As Matthieu's answer shows, blockcypher.com's API includes the time that they first saw the transaction. This suggests that the actual time three confirmations was reached was around 2014-05-03T09:31:55.867Z, approximately 59 minutes after the transaction was created (since it was relayed by Blockchain.info, I'm assuming the transaction timestamp there is accurate).