Many offices use a single TextUs Account with multiple users having access. Individual users will have their own login but they will be working in a shared environment.
Users are able to see if a teammate is responding to a Contact. You will see "Response in Progress" appear in the Conversation list if someone else is typing a message to that Contact.
Please note that if another user on your Account has the same conversation already open when a message is received, the message will automatically be marked as read.