To clarify, they are billing you ten days before the bill is generated, or ten days before the actual due date? Whenever I've had automatic billing from a company the bill was charged the day it was generated, not the actual due date, as the due date is really the LAST day you have to pay it before incurring late charges. So, in my experience at least, when a bill was generated on May 5th and was due on June 5th, it would be charged to my checking account on May 5th.
To add, I've never had automatic payments with Hughesnet. I've always paid the extra $5 (God only knows why we have to do this) to have the ability to pay it manually.