Yes, you do. When you use the multi-user functionality of the Modeler, the project database is stored in a PostgreSQL or SQL Server database that is shared by all users, i.e., every user works directly on this database. Whenever you save a certain document (a microflow for example) to the database, the other users will also see your changes as soon as they refresh or open the project. As a consequence, if there are consistency errors in the project, every user will see those errors, and no one will be able to deploy until those errors are solved.
You can prevent this situation from occurring as follows. When you open a project, the Modeler reads the entire project from the project database. After that, you will only see changes by other users if you refresh your project. So if you make sure that you only refresh the project in the Modeler when everyone has solved their errors, you can always deploy.
Edit: Please note that the 'Auto-refresh' button on the messages dock has nothing to do with refreshing (i.e., updating) the project from the project database; rather, this option causes the Modeler to recheck model consistency (i.e., refresh the messages list) after every change you make to the model.
If you see the errors of other users in your Business Modeler you can not deploy. However, you do not have to refresh when you deploy. Refreshing means retrieving all changes available in the central repository.
So, two options: