The frets should already be installed before the action is determined. String action is set by adjusting the height of the nut and bridge relative to the tops of the fret crowns, so the height of the frets doesn't affect the action of the instrument. 

It should be noted that there are members of the zither family which have raised fretboards but which are not mtn dulcimers, for example concert zithers.

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Here's a Folkcraft Chromatic Dulcimer. It's still a Dulcimer because it's part of the Zither family in which the fretboard is above the body as opposed to extended from the body like a Guitar so keep that in mind. The 4 string setup w/ the Doubled Melody String is a bit easier to play w/ Jumbo Frets because the larger sized jumbo frets reduce the distance between the strings & the frets allowing for easier action.