Best practice for saving multiple users' data locally on device (Or is it necassary?)

My app has a chat feature, and the chats are held in SQLite. Currently this is an issue if multiple users use the same phone. Chats from all the users would show up in the past message areas, although the messages would appear to be sent from the person who is presently logged into the app. My question then is: How do apps generally deal with this issue? Or do they assume most people will login to the app from their own device or create another user account on the device itself -- therefore leaving the problem to the device user since it is not a normal problem?