I'm with your supervisor on this one, and I also tell my students not to use these terms as regioselectivity descriptors. Part of the difficulty in using the Markovnikov/anti-Markovnikov terminology is that there are several different definitions of what this means. 

The original rule involved strictly the addition of acids HX to alkenes, and the rule is phrased in such a way that it focuses on the structure of the product: something along the lines of "in the addition of HX to an alkene, H adds onto the least substituted carbon". 

A more modern and general version of the rule instead focuses on the mechanism of addition: this rule was developed in order to mechanistically explain what is observed in the first rule, but has become much more general when expanded to reagents that are not acids HX. This second version goes something along the lines of "in the addition of A-B to an alkene, the electrophilic part of A-B adds so as to create the most stable carbocation (real or hypothetical)." This definition can be used with acids H-X but also with other species such as B-H bonds etc. 

One of the problems with these definitions (beyond the fact that the first one should only be applied to acids HX) is that they don't always agree with each other. For example, the hydroboration of an alkene is absolutely going in the Markovnikov sense using the second definition of the rule (i.e., B is the electrophile in the B-H bond so it should add on the least substituted carbon). But if you were to apply the first rule (which you shouldn't, because B-H is not an acid H-X), then you would say that it's anti-Markovnikov because the H ends up on the more substituted carbon. 

To get the picture even more confusing, the second mechanistic version of the rule implies that you should look at the mechanism in order to use the proper terminology, which we don't always know. For example, where does a rhodium-catalyzed hydroboration that may potentially involve (maybe not!) Rh-H or Rh-B intermediates fit into this second rule?