Even though I don't know what these particular potential functions represent, the causal relationship is easy to calculate, but is complex and not trivial. He is right and wrong. My simple tool collection does not include this group. Yet the concept that requires this idea is essential. This group is part of the machinery that makes possible causal measurements of lengths in various topologies.
Metrics change due to local conditions.
The concept of a flexible, causal metric must be preserved. With quaternions, causality is always found in the scalar of the square of the difference. For two events in flat spacetime, that is the interval. In curved spacetime, the scalar of the square is different, but it still is either positive, negative or zero. The Problem of Time Time plays a different role in quantum theory and in general relativity.