You need to configure this yourself, as you have both options: return a case to the Omni queue OR leave it with the last user who owned the case.
For 'keep it with the last agent' option you don't need to do anything. When a case will be reopened, the owner will receive notification the same way a new case gets distributed (Omni-channel pop-up). The only difference is that only the owner of a case will be able to take it.
For the 'redistribute case between agents' option you need to return the case to the Omni queue. The obvious way to run a flow/process to update the owner is not the best option though, as the combination of Case Assignment Rules and page layout case assignment will do it for you.
So, if you want the case to be returned to the Omni with a reference to the last owner you need:
- Configure Case Assignment Rules to put the case into the Omni-enabled queue
- Set the 'Default' checkbox under the 'Case Assignment Checkbox' section of the layout properties to true on the page layout