Visual effects supervisors are generally the highest-ranking employees of a contracted visual effects house to be in day-to-day contact with the director and production team during all stages of production. They act as a buffer between directors, producers and actors, on the one hand, and visual effects technicians, 2D and 3D artists and CGI experts, on the other. It's their job to relate to key creatives how certain effects can be achieved and for how much time and money — and to make sure that principal photography proceeds in an efficient manner for the later inclusion of visual effects.
Directly underneath them, at least during principal photography, are on-set visual effects supervisors, who particularly deal with problems of setting up shots properly to accommodate later visual effects, often realised through CGI.
Mark Murray was also the uncredited VFX supervisor for Milk VFX.