The time zone is indeterminate at those points, of course.
Rather like asking which way is east or west at the poles.
So, do people working there follow any time and date?
It varies. Some research groups use the time of their home country, others use the time of the nearest inhabited part of the world.
Because every line of longitude meets at the poles, I would say that the time zone follows GMT time, or in other words, British Winter Time
But why pick the time corresponding to 0 longitude, rather than any of the others, since they all pass through the poles?