Well the exchanges that participate in the Tether blockchain each run a node or nodes. The transactions are cryptographically verified, so there's a common ledger between all these participating exchanges. But Tether has a couple theoretical weaknesses due to this setup. A quorum of exchanges could theoretically collude to manipulate transaction history or shut out other exchanges. And Bitfinex itself is the centralized holder of the USD backing Tether, so that makes it very vulnerable to any shortcomings in Bitfinex's accounting. Ultimately to cash out Tether the exchanges have to go to Bitfinex and request a fund transfer so they are a single point of failure for the Tether chain.
There are certainly some trust issues with Tether, but in this case I don't think that exchanges could easily roll back Omni transactions unless they were to fork the Omni protocol. Omni transactions happen on the Bitcoin blockchain - they are effected by extra data in otherwise normal bitcoin transactions. In order to roll back the Omni transactions you would have to either (1) roll back the underlying bitcoin transactions or (2) convince everyone who runs Omni nodes to update their software to your branch which discards the transactions you wish to roll back.
Option (2) has already happened. Tether got hacked and someone issued/transferred lots of coins to themselves. In response, the whole omni network was upgraded to blacklist these stolen coins!
