looking at the moment coefficient for certain NACA profiles, I noticed that their graph changes with AoA and is not a constant horizontal line as I would expect (pure moment independent of the AoA). This seems to imply that the moment and the associated moment coefficient is measured relative to a point $P$ (maybe the leading edge $LE$?) that is not the aerodynamic center $AC$ (otherwise the moment would be independent of Aoa) but I am not sure what that reference point may be. The figure below illustrates what I discussing...
Its most likely from the AC. When it is said the moment does not change with AoA in AC it does not imply a completely straight line, it can vary a bit but is somewhat straight as yours also is around 0.1. And that 'rule' only goes for low speeds btw. Once AoA is increased above a certain point when separations effects come into play, it will no longer be 'straight' as your graph also shows around 8 degs.
If you think the line is not straight enough, maybe your AC is not calculated exactly (maybe it just uses the rule of thumb of 1/4 chord).