Your bitcoins go into a localbitcoins controlled excrow. Only release the Bitcoin from escrow when the cash is in your hands. If there is any issue with the payment you can dispute the transaction and your escrow will be returned to you.
If you ever need help with ANY dispute, I am an expert at resolving them and have worked with LBC admins for several years.
Oh, I see. Thanks for clarifying. This will be a great alternative to Coinbase!