In the backing report for any VAT return (cash or accrual) QuickFile will show the invoice date, however for cash accounting method the calculations are always based on when any associated invoices were paid.
If I look at the VAT return 01/07/2015 to 31/08/2015 this was indeed calculated on a cash basis, this is indicated at the top of the CSV report.
When you file your first return QuickFile will bring forward any earlier entries beyond the start date (in the case of this account 01/10/2014). All payments attributed to #QF00168 occured after the start date and were brought forward to the first return.
I don't see any problem with the VAT calcs for that return, you could always drill down on the payment list for that invoice and provide a detailed breakdown of the payment schedule if required.