Smoothing the mortar eliminates the gaps in the mortar left by the trowel notches thereby increasing the surface area of the mortar that is in contact with the tile. -- amateur

That makes sense logically, but I’ve read the ridges are what creates the hold. Otherwise, what’s the point at all?

I don't understand smoothing the ridges. Use of a notched trowel is to keep the amount of setting material constant over the field of the tile. They also allow for some give when setting each tile. The final result of setting, bumping, leveling, etc. should push the tile into the thinset so that entire surface (or close to it) is covering the tile.

Ditto Seaborn. All I can figure is that smoothing the ridges might minimize what can squeeze out between tiles, which I would appreciate!

Glad I’m not the only one confused. So, are we in agreement that I should or should NOT follow the directions and smooth the ridges?

Well, It's hard to contradict the manufacturer's written instructions. Maybe it'll make sense when you do it.

Ditto again.

The manufacturer has used generic instructions for a glass mosaic tile for all of their mosaics. A white high quality thinset and proper setting, with directional troweling, will have the ridges collapse as the stone is bedded into it. It’s only the edge spacing in glass that will telegraph the ridges of unsmoothed thinset. Marble does not have that issue, if the installation meets TCNA standards for coverage.

This is when your tiler does a coverage test, and peels one back off, to show full coverage, with collapsed ridges. Thinset that has skinned over and is too old in the bucket, loses its stickiness and should be discarded. This is why you hire a master tiler, who mixes only what can be used within a certain time. Directional troweling, with the right consistency thinset, is superior to a backcombed bed.