I have found out the likely reason that tactile paving markers on dual-use paths are the wrong way round!
A page on the UX StackExchange discusses tactile paving on dual-use paths and the best explanation is that it can be uncomfortable to walk on longitudinal ridges, whereas transverse ones are OK.
(Apparently the usual terms are "tram" vs "ladder".)
I occasionally get a painful twinge in my ankle when I tread on the edge of a badly laid paving stone, so I can sympathise. But surely tactile paving is supposed to be felt by the feet, so it should not hurt people who tread on it even inadvertently!
Tony Finch – blog