Unless you have a Family Sharing level subscription and other people are part of your Family Sharing group you will probably find that if more than one person at an one time tries to use the service with the account that holds the subscription that others will be told by the system they cannot get access to it.
Make sure that each family member has a unique Apple ID as suggested in this support article --> Make sure that each family member has a unique Apple Account - Apple Support
This support article describes how to create a new, non-child Apple ID = create an Apple Account. --> How to create a new Apple Account - Apple Support
To learn how to set up Family Sharing, read this support article --> How to set up Family Sharing on your iPhone, iPad, or Mac - Apple Support
Click on this link to read how to 'get an Apple Music Family subscription --> Get an Apple Music family subscription - Apple Support