Customers who activated their DigitalOcean account by entering a credit card are automatically charged (if they owe any money after the credit has been used up) on the first of the month for the total of their bill.
Paypal users get sent an invoice on the first and are asked to pay through paypal for the servers, after the credit gets used up.
The reason you have $9.99 in credit left after creating 2 VPSs is because droplets are charged by the hour (https://www.digitalocean.com/pricing). So right now, what you are seeing in your account is the cost of 2 servers, at whatever size you chose, for a couple hours.
If you run each server for a month (non-stop), each droplet is billed per hour up to its monthly cap. This is actually a little less than the cost of the server for all of the hours in the month. It's usually like a day free or so.