Pinking edges of seams and interfacings is an old sewing trick. The 'broken' edge leaves no real line that can show on the right side as a ridge when pressed.

The soft interfacing that you've seen in jackets may be a bit too thick to use with this tartan. There are thinner and softer interfacings available.

As an addendum to my method, make sure that the interfacing is also a non-woven to prevent raveling of the interfacing edge.