In doubles, the captain's card is reserved for the whole team when they sign up. The partner can pay their own share from the email or the app. Any share still unpaid when the payment is charged is charged to the captain.
If you're the captain
When you sign up, the full team entry is reserved on your card.
It is charged about 4 hours after the round starts, or 6 days after you signed up if that comes first.
At that point you're charged your own share, plus your partner's share if they haven't paid it.
If you're the partner
You get an email saying your team registration is one step away, with a Pay button. Your share also shows as Unpaid under Profile → Purchases.
Pay your share before the round starts if you've agreed to pay for yourself. If you pay first, the captain only pays their own share.
If you're not sure whether your share has already been paid, check with your captain or the club before paying.
Singles and teams the club adds
In singles, you pay your own entry.
If the club adds your team, for example from the waitlist or into the next round, each player's share starts as Unpaid. Pay it from the email or Purchases.
Good to know
Prices can differ per player, for example for members.
A club wallet can only be used at sign-up if it covers the whole amount reserved (the whole team entry in doubles).
Your partner can pay on the player website from the email link.