To be able to listen to music at the same time, all family members need to have their own Spotify account. If they don't have their own account yet, they can sign up here.
Once all family members have their own accounts, you can then invite each member to your Premium for Family plan by following these steps:
Once each family member joins the family plan, they should be able to enjoy the Premium features with no issues.
However, you'll need to make sure that, if they're accepting the invite on the same device it was sent from, the owner who sent the invite has logged out of their account page first.
For more information regarding the Premium for Family plan, check out this support article.
This Spotify Answer was submitted by @Noah.
Didn't help? Search for more Spotify Answers, or create a new thread and ask the Community.