Any person added to a group by import or manually typing, will be started in any corresponding active workflow steps. They will then receive any immediate messages that are setup in the automated workflow, and their timeline will start for the messages set on a wait schedule. The timing is all based on when a person "is added to the group".
To double check a message is active, go to the Groups page, click on the specific group in question and then click on automated workflows. Then you can see in the list of steps if there are active on the right side of the list.
To make it active, click inside of the message and make sure the check box at the bottom is checked to make it active. Make sure you save any changes. Activating a message will follow it's schedule and start sending immediately. If a person was added on the same day you make it active, any immediate messages will send after making it active.