ProTip from Jon, a ShapeShift Developer:
Omni and Counterparty transactions (and their associated assets) all happen on the bitcoin blockchain. That's pretty cool but it means that looking up information about what happened in your transaction can be tricky.
If you look at an omni transaction on the bitcoin blockchain it looks like you sent a tiny amount of bitcoin (you did!) but it wont show you anything about your omni transaction. So if, for example, you send 100 Tether (USDT) which is an omni asset and you look at say blockr.io the transaction may say 0.000002 BTC.
The trick is you need to look at a special omni block explorer (like omnichest.info) which will show you the tether transaction amount of 100 USDT. The same applies to counterparty assets or any other type of cryptocurrency that uses the bitcoin blockchain.
Good luck and happy exchanging!