Hi modernlooktiling,
When you connect QuickBooks Online with the ATO, this will enable E-lodgment for your BAS and gets reported to the ATO. As for the GST payment, it is for recording purposes only in QuickBooks. You'll have to log in to your ATO Access Manager and process the payment from there.
You can refer to these links to learn more about BAS e-lodgment:
Drop by again if you have concerns about your BAS in QuickBooks Online. I'll be right here to answer them for you.