Well, yes: stockinette always curls at the edges.
But this pattern only uses stockinette for two rows at the edge, then moves to a drop-stitch pattern, which should be looser and more relaxed.
I think the problem is with the yarn substitution.
The original yarn, Softwist, is 49% merino and 51% rayon – drapey and soft by its nature. The substitute yarn, Encore is (if I recall) 25% wool and 75% acrylic. You are just not going to get the same results with yarn that’s so different, even if the gauge is the same.
Whenever you plan to substitute yarn, you really [color=red]really[/color] have to knit a big swatch of the new yarn in the design’s stitch pattern to see if it is going to behave the way you want it to. And you really [color=red]really [/color] need to wash and dry the swatch as the label directs to see how it reacts.
Encore doesn’t block well because of the high acrylic content. But a trip through the washer may help (IF the Zen ribbon is machine washable; if not you’ll have to hand-wash). Lay the damp poncho on a couple of towels and pat the edges firmly – beat them into submission, so to speak.
Or take it to a good dry cleaner and explain the problem. Be sure to tell them the fiber content. Professional steaming may do the job, but I wouldn’t try it at home. Nothing like melted acrylic to ruin your day.
Hope you find a solution – it’s such a pretty poncho.