If you notice $0.00 in the backups console, there's no need to open a support request. It's not a bug. At 15 cents per gigabyte, if you have just a few megabytes of data Amazon doesn't charge you anything.
Backups start from around 100KB for a freshly installed TurnKey appliance. Remember, TKLBAM only saves changes you've made since the appliance was installed.