There are no options to adjust the exact time invoicing is run in Fusebill for your account. The time that invoicing/billing takes place in your account is related to the timezone that your account is in. Billing typically takes place after midnight of the same day in order to process a very large amount of information.
While the option is available to adjust the timezone of your account, this may have unforeseen consequences around billing timing and may not have the desired outcome. There may also be errors in billing if you do this.