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.