They were asking for privacy so their username was hidden from user lists. This is the only modification that was made for them.
This is a change address, so this is the money returned to the pool's wallet. From the numbers which you quoted:
37.68105879 BTC transaction minus 12.66769504 BTC payout = 25.01336375 BTC change.
And it's exactly these 25.01196375 BTC which you found.
This is how Bitcoin works. You can only spend whole outputs of previous transactions, you cannot spend some part of it. If you want to spend less, your wallet just uses a change address where change from the transaction is returned to your wallet.
Most likely you will see this 1HAQpP7D1eTbMhu5WvkQxZmRWNHF2AEYMt address sending payouts to users tomorrow or a day after.
I can show you how it was in the past:
March 26, 2014 1:32am payout:
https://blockchain.info/tx/7e2edeaf3457f170467fd5ba2b10b8527e83b98d812be20f779677f2395945dc22.11547462 BTC sent to users as reported by CleverMining website
27.01426284 BTC moved as reported by blockchain.info
This includes 4.89878822 BTC sent to 17nAyN7CUDhTT5LZT5C6VKhZUvi3LxN935
which is not an user at CM:
http://clevermining.com/users/17nAyN7CUDhTT5LZT5C6VKhZUvi3LxN935because it's a change from this transaction: 27.01426284 - 22.11547462 = 4.89878822
One day later, March 27 payout:
https://blockchain.info/tx/88643eca70ebc081549be4eed55061d88ad3abc739511a52308b97768ad97435?show_adv=trueBlockchain.info has also an “advanced mode” which is enabled in the above link.
Please check what addresses this payment was sent from. In advanced mode you also see amounts coming from each addresses.
As you can see, the mysterious non-user 17nAyN7CUDhTT5LZT5C6VKhZUvi3LxN935 who got Bitcoins from March 26 payout contributed to sending March 27 payout and it sent exactly 4.89878822 BTC.
This is because 17nAyN7CUDhTT5LZT5C6VKhZUvi3LxN935 is one of CleverMining's wallet addresses and it received a change from one of previous transactions. This change was sitting in our wallet all the time and was used to send next day's payout.
This is Bitcoin change addresses work.
You can think of Bitcoin inputs/outputs as physical bills, with the only difference being that you can cut Bitcoin “bills” into pieces and make them infinitely divisible. But when you want to spend only some part of a bill, you need to cut it and do something with the part which you are not sending. If you received 1 BTC from someone and you want to send 0.8 BTC somewhere, you need to cut that 1 BTC bill into 0.8 BTC bill and 0.2 BTC bill. You send 0.8 BTC bill somewhere and put the 0.2 BTC bill back in your pocket. Blockchain shows this as 1 BTC sent to two addresses getting 0.8 BTC and 0.2 BTC respectively. The 0.2 BTC is a change from this transaction and it's back in your wallet.
Blockchain.info doesn't know which addresses are change addresses. It only sees X Bitcoins moved. Most transactions actually have Y Bitcoins sent somewhere + Z Bitcoins returned to the wallet as change. Y + Z = X. Blochchain.info shows you X Bitcoins moved as it cannot know which of the output addresses belong to the same wallet as input addresses.
Why are there so many discrepancies in these transactions?
Why does the front end accounting not match up with the back end accounting?
Should we be concerned about the accounting methods being used?
How can we know if we are properly being credited for what we are due?
What other things are being concealed from us miners?
What else do we have to worry about?
There are no discrepancies and accounting matches perfectly what's shown on the public Blockchain.
Your questions are because you apparently don't understand how Bitcoin works. That's fine, because most of Bitcoin users don't understand.
I believe other users can point you (and others) to some ELI5 explanation on how Bitcoin change works. I couldn't find any link quickly. My explanation using the bills analogy was above, but I bet there are better ones somewhere.