Hi Sweetwilliam,
It's a really good (and interesting) question. Essentially you are correct. The funds are set aside in some form of holding account - similar to the way a checking account is separate from a savings account.
The two parties send one on chain transaction into a "multi-signature address". The balance between the two parties is sorted out at a later date.
A general summary of how this works is found here
Funds are placed into a two-party, multisignature "channel" bitcoin address. This channel is represented as an entry on the bitcoin public ledger. In order to spend funds from the channel, both parties must agree on the new balance.
The more technical/specific explanation of how it works is here
Two parties send an initial amount of Bitcoin into a multisignature transaction with a local consensus on the current balance allocated between the two participants.
One onblockchain transaction is made to deposit the funds into a multisignature output. Before this transaction is made, a refund transaction is created, which returns the original deposit to both parties.... In effect, they have created numerous "double spends" from an onblockchain transaction, but have elected not to broadcast the spend until either party wants to redeem their funds onchain.