The images at bottom show suggested placement (or map as I’ve taken to calling them) of fusible interfacing that is typical of a mid to higher price point lined vest with welt pockets. The sample garment (style #22200) is shown at right.
Keep in mind that there is always variation in practices between manufacturers owing to desired or expected garment performance. In this case, the vest (being a split suede) is a 2 oz garment weight leather -which isn’t noted for keeping its shape without a little assistance. Hence the fusible. And yes of course you can press leather, don’t fret so much over it. At close are links that provide back story should you need that but suffice to say, I’ve become partial to knit nylon tricot fusible. It sets quickly (no, we don’t hold the iron down for a count of x) and neatly with a bit of steam. I also fuse without a pressing cloth but then my iron has a teflon (or is it silicone?) shoe so nothing sticks to it.
As you should note, all outside edges are fused. You should also note that in the case of partial fusing (the center front and front facing are fused in their entirety) I prefer to curve fusible pattern pieces because straight lines are more easily discerned from the face side of the product. The side front fusible is a departure because it has the welt pocket running midway through the piece. That will be okay because the pocket will mask any unsightly lines that may show up there.