Confusion about which agent is working on a ticket is usually prevented by:
If an agent wants to prevent other agents from changing a ticket, they can use the Deskpro locking feature to manually lock the ticket.
You can also enable automatic locking of tickets from Tickets > Settings. When this is enable, a ticket will be automatically locked when an agent opens it in the content pane.
Automatic locking can be useful if you find that agents both trying to reply to the same ticket.
The lock timeout is the period of time before the lock is automatically removed. It applies to both automatic and manual locks. This prevents locks being left on too long (for example, if an agent locks a ticket and then forgets about it).