As mentioned in this article, new members can join a group with installments even after one or more installments have been paid. When this happens, the participants that were already charged before the new members joined will be charged less for future installments. This ensures that everyone pays their fair share of the purchase in the end.
As an example, let's say you're participating in a purchase with a total cost of $600. There are two payment installments of 50% each, and three people (including yourself) committed to paying an even share of the total cost. Your total share of the purchase at that time is $200, and your first payment is $100.
After the first installment has been paid, three more people sign up to pay for an even share of the total purchase amount. Now, your total share of the cost is $100. Since you've already paid that amount for the first installment, when the second installment is paid you have no remaining balance to your share and are not charged any additional amount.
If you paid more than your final share amount due to new group members joining the purchase, Pay By Group will automatically refund you the difference between what you initially paid and your correct new share. Such refunds will be triggered at the same time as payment of the final installment.