I do have Vitz 2012 i a believe both have 1KR-FE engine 996cc
The only suggestion I will give it to you is try to fill up high octance (8-10 Liters) and see difference in mileage then, if you saw improvements hopefully you will (1-2KM/L) then this is the true mileage on regular petrol.
It's a 996cc CVT and the average of 13 in city seems fine. You can do regular maintenance once completed KMs/time. No need to spend money if its already done recently..
I am using 0W20 and my route is very stop and go traffic I hardly get 9 -11KM/L depending upon traffic.