It was a gradual thing, like all fashion changes.

The first real documentation I can cite for the use of the side, or knife pleat is when the Gordon Highland regiment began making their kilts this way in 1853. But that doesn't mean that this manner of pleating was invented in that year!

Nor does it mean that everyone began knife pleating their kilts in 1853, either. In fact, if you look at the famous portraits by Kenneth MacLeay, done in 1865-9, they all show box pleated kilts.

The Book of the Club of the True Highlander, published in 1880, states that the "newer" form of pleating (i.e. knife pleating) is incorrect, and that kilts should properly be box pleated.

And let's not forget that up until the amalgamation of the the Highland Regiments, some still wore box pleated kilts, the Seaforth being one prime example. Though doubtless by the time we get to the twentieth century knife pleating was by far the norm.