How to determine the configuration of an propargylic alcohol?
I think your working is correct, and the molecule should be assigned as S, with the alkyne taking priority over the disubstituted alkene such that the priority goes:


alcohol
alkyne
alkene
hydrogen


This leads to the S configuration, as you propose. 

There is a chance that your supervisor is confused because in IUPAC naming nomenclature, the alkene often (and indeed, in this case) takes priority over the alkyne, which would of course lead to assignment of the molecule as R.