The datasheet from ST says for Vpp -2 to 14 V and on Vcc/Vio (except A9) -2 to 7V.
So you are in the specific range.
These are absolute maximum ratings not typical voltages needed for a proper programming. You can't program a chip with VPP=2V for example. The datasheet is clear about programming voltage: 12.75V ± 0.25V. The VCC voltage while programming should be (according to the datasheet) 6.25V ± 0.25V.
I simulated a chip write (i don't have this chip though) with a 150ohm load resistor between VSS and VPP (~100ma current for the Vpp) and 150ohm for VCC (~50ma).
The VCC voltage was ~6.9V during write and the VPP was about 13.8V.
Here is a snapshot of the VPP for the old TL866A
And here is the newer TL866II+(XGpro)
Both programmers use the same 50uS Vpp pulse width in the main interface but the total programing time is about twice for the TL866II+(~300sec for TL866II+ vs ~150sec for the TL866A/CS). From the waveform we can observe that for the TL866A a programming pulse is Ton=60us +Toff=20us (80us/cell) and for the TL866II+ Ton=Toff=63us (126us/cell).
Despite all these differences there should be no problem.
@Circlotron can you hook a single Xgpro (TL866II+) programmer with one of those problematic chips and post what the error is when fail?