Yes, essentially all cables cross on the right side row (the row facing outward as you wear the garment). For the first set of cables, the side cables, the pattern is p1k4p1:
"Repeat rows 1 and 2 working a C4B on the middle 4 stitches on 3rd row (not counting seed st) and then every 4th row. These 4‐stitch cables will form the side seams."
So the cable cross in on row 3 and then row 7, 11, 15 etc., all RS rows (or knit rows in the main body of the vest).
And yes, that means the last side you knit is on the wrong side or purl row in the main body of the vest.
There's an open flap in the center back and one in the center front after you join to knit in the round. Don't close it up if you want the look of the pattern picture. If you don't like that open vent, then just seam the vent closed. It's very neat the way the two pieces are joined at front and back with the cable cross (although, for me I think there's a typo that confuses right and left needle in line 10:
"On the last row, stop while there are still 4 sts on
the left needle. Join pieces into the round on the next row as follows. Slip the 4 sts remaining
on the right needle onto a cable needle and hold in back...")
Long story but nicely done pattern. Enjoy it!