Many thanks for the file Beanzvision.
So just to confrim, after checking Beanzvision's scene I reasured myself that in order to make the tile colour to be visible on vertical displaced edge you need to use different values for tile gap&blur in base colour and displacement. Generly speaking, base colour values for gap&blur size have to be smaller than dispalced value. This makes the displaced area slightly smaller than the colour area and thus it projects colour onto vertical faces.
Scene units have not much to do with it. (Maybe except for the fact that if you're using meters you need to allow max to use more than default 2 decimal places to use low values like. 0.001 or 0.0001 for better control of transition point)
The above method works but is not an ideal solution as you cannot drive tile shader with just one tile map but you have to use multiple ones to achieve desired result.
I think Romullus' idea of colour bias control would be a great adition to tile map controls.
Maybe we could have additional colour bias control which would shift tiles/grout colour transition point to either direction, because most of the times you want tile walls to have either one colour, or another, but not a smooth gradient. Beanzvision's method if it works, it does so in very specific case, which is hardly practical at all.