In my understanding, they have the account numbers and can do ACH withdrawals - just like someone who has your debit card number (but against a checking account, not a card). So I believe it's like every other transaction (or check) - there's an intentional (as I get it) processing period for a day or two, and you can always call your bank and request to not honor it. I could be wrong though.
And actually, they can be associated with a debit card instead of a bank account - they've failed to associate with my bank, so I have had to go this route (and there's no way to switch it afterwards).
Oh, and I totally agree that arbitration clauses without a way to opt out are disrespectful to say the least.