This is bad. It'll badly affect people with low bank balances and high overdraft charges - it'll be interesting to see how Twilio reimburses people for charges banks levy on customers.
Debit/bank users are definitely the most susceptible.
So I would wait and see, how this is handled. I see updates about every half hour, so I suspect, that they will handle the rest as transparent as well...
Disclaimer: Not a customer.
We'll have more on what caused this incident and what we're going to do to make it right later today.
OP link directs to the board with our up-to-the-minute status on resolving this incident.