I don't use dimensions very often, but I would guess that value is being defined by the selected spatial reference of the feature class. I tested adding a few dimension layers to a project, and that seems to be what determines it.
Even though there is a "Map Units" dropdown when you create a dimension feature class, the documentation states that "The units should match the map coordinate system." Furthermore, I can't see where the selection there is actually maintained in the resulting layer. Opening up the properties only shows your selected reference scale and any styles you've defined, nothing about units.
So you'll need your dimensions in a spatial reference that uses feet as the linear unit. Since Pro reprojects layers on the fly, there's no issue in using that layer in a map that is itself in meters.
- Josh Carlson
Kendall County GIS