(-ve)Mill Tolerance % is used in minimum wall thickness calculation.
Only when IGE/TD/12 code is in effect, this tolerance is used to reduce the cross section against which stress calculations are made.
That means when we are analysing line in code other than IGE/TD/12 the (-ve)Mill Tolerance % will not be used(inspite of defining it) to reduce cross section and we are making the stress system safe with nominal thickness.

I have analysed FRP line (UKOOA code)with nominal thickness(defining nominal thickness in Wt/Sch field) and defined (-ve)12.5 % mill tolerance and given for vendor's approval.

Now the FRP vendor is insisting to run the system on minimum thickness, which is nominal thickness minus 12.5 %.
i.e defining minimum thickness in Wt/Sch field.

Is the vendor's point correct?

Unless you are analyzing your system to a specific piping code which instructs you to deduct mill tolerance for the stress calculation, I'm going to disagree with your vendor. Most piping codes state that you are to use nominal dimensions when performing a flexibility analysis. Then, depending on the code and the load case, you sometimes reduce the section modulus for the stress calculation.

Mill tolerance should be considered up front, when the pipe wall thickness is sized. Once you increase the thickness to account for mill tolerance, you use the final (thicker) thickness in the computations. This provides a larger stiffness (conservative) and a larger dead weight (conservative).

If your vendor insists on considering mill tolerance, you could enter it as corrosion, then set the "ALL_STRESS_CASES_CORRODED" directive in the configuration to "checked". This will reduce the section modulus for the stress check, but use the full cross section for everything else.