Hi Frankie Yuen,
Welcome to the Apple Support Communities!
In order to have an Apple Music Family plan, you must have an iTunes Family Sharing account set up first. You, as the organizer, would be responsible for your family's purchases in the iTunes Store, App Store and iBooks Store. However, if your family members purchase physical gift cards in local retail stores, and redeem them on their individual Apple ID accounts, the gift card would be used before you would be charged for any purchases.
Here's some information to help you determine what the best option is for your family:
Set up Family Sharing
Family Sharing makes it easy for up to six people in your family to share iTunes, iBooks, and App Store purchases, an Apple Music family membership, and an iCloud storage plan, without sharing accounts. When the family organizer turns on purchase sharing, you can pay for family purchases with the same credit card and approve kids’ spending right from a parent’s device. Family Sharing also lets you share photos, a family calendar, and more to help keep everyone connected.
Get an Apple Music Family subscription
Each member of an Apple Music Family subscription gets unlimited access to the entire Apple Music catalog, music recommendations tailored to their personal music tastes, and access to their own iCloud Music Library, which makes it possible for them to listen to their music on all of their favorite devices.
One adult in the family—the family organizer—can set up Family Sharing for the group from their iPhone, iPad, iPod touch, or Mac. If you turn on purchase sharing, you'll be asked to confirm that you agree to pay for purchases initiated by the family members you invite and that you have a valid payment method on file. Valid payment methods for setting up Family Sharing include credit cards and debit cards.*
After you set up Family Sharing, you can invite additional family members to join your family group.
After the invitees accept your invitation, each member of your family group will have access to Apple Music.
If you already subscribe to Apple Music, you can change to a Family Membership in the Music app or in iTunes on a computer. Learn how to manage your Apple Music subscription on your iPhone, iPad, iPod touch, Mac, or PC, or on an Android phone.
Family purchases and payments
How iTunes Store purchases are billed
If you have gift cards or content credits
If you use a gift card for a transaction, the amount is deducted at the time of your transaction.
When you make a purchase, content credits are used first, as long as the value of the item that you're buying is less than or equal to the value of the credits. Any gift cards are used next. If your gift card is less than the total cost of the purchase, the payment method that you have on file is billed for the remaining balance.
If you have no content credits or gift cards, the payment method that you have on file is charged for the entire purchase.
Use Apple Music on your iPhone, iPad, iPod touch, or Android phone
Add and download music, shows, and movies from the Apple Music catalog
Take care.