Are you switching your plan to family or are you joining another family plan? I can't say for sure but I think what might happen would depend upon if you are changing a membership or canceling one and joining another.
Manage your Apple Music membership on your iPhone, iPad, iPod touch, Mac, PC, or Apple TV - https://support.apple.com/HT204939 - Change your membership > "With a Family Membership to Apple Music, families of up to six people can enjoy all of the benefits of Apple Music, each with their own library. ... To use a Family Membership to Apple Music, you must set up Family Sharing on your iOS device or Mac. "
Set up Family Sharing - https://support.apple.com/HT201088