Do I get notified anytime someone joins my group?

No. We did not want to overwhelm group administrators with notifications about players joining their group. You will only receive a notification if your group is a request to join group, and somebody has requested to join it and is awaiting your approval.

How to make your public group a “request to join group”

Go to your group’s settings (via App or Web) and select the setting “User requires admin approval to become a member”

Notification you receive

Notification when somebody requests to join your Public “Request to Join” group.