you would need to look at all the outputs of bitmixer over the next 12 hours that add up to 2,224.354937 BTC (99.5% of 2,235.5326 while adding .0005 to each output in order to figure out where that person's money ended up.
I've never looked into how mixers work, but it seems pretty obvious that you would only allow withdrawals of particular sizes. If you want to withdraw 2,224.35x BTC then maybe you have to make 2 withdrawals of 1000 BTC, 2 of 100 BTC, 1 of 10 BTC, 4 of 1 BTC, etc. Then your plan of "look at all outputs that add up to ..." fails immediately, since all the outputs are of generic sizes.
Bitmixer does not use "accounts" you go to their website, tell them which addresses that you want them to send to, tell them what percentage each address should receive (12.346% to address "A", 36.257% to address "B", and 51.397% to address "C" - for example), you give them a time delay for each address (zero for address "A", 4 hours for address "B" and 2 hours for address "C"), then they give you an unused address they have the private keys to for you to send to. If you were to send 100 BTC to that address, then they would send 99.5 BTC to those addresses with the corresponding percentage minus .0005 BTC for each address. They claim to mix tens of thousands of BTC per week so if you only mixed 100 BTC then there would probably be a lot of possibilities as to which outputs belong to you. However mixing thousands of BTC would probably give them less privacy.
Bitmixer has since changed how they work so you can customize the fee they charge so an onlooker doesn't know exactly what the total sum of outputs will be exactly.
Figuring out which addresses belong to Bitmixer in itself would probably be a difficult task because they do not reuse addresses.
I believe that bitcoinfog uses an account system, I am not sure exactly how they work, however I know that they make heavier use of old addresses (they reuse addresses) and I don't think they send outputs in even amounts like that because they have such a wide range of how much money they mix for their customers (some only want .5 BTC mixed while others want 50 BTC mixed).