Note: Regular Kihnu Troi cast-on can be found in “Cast-on, Bind-off: 211 ways to begin and end your knitting” by Cap Sease, p.59.
Please note some youtube videos utilize a crochet hook instead of a right-hand needle for this cast-on.

Reversed Kihnu Troi cast-on (i.e. going in the opposite direction than the regular one) is ridiculously easy.

Step 1. As usual, make two separate slipknots and place them onto left needle, with MC one to the left of CC one. In this demonstration teal yarn is MC and orange yarn is CC.

Step 2. Keeping both working strands in back, knit CC stitch with MC yarn. Place MC strand to the right, pick up CC strand under MC strand (still at back), make CC yarnover and knit MC stitch on the left needle with CC strand. Return CC stitch back to left needle, then pull MC strand to tighten the stitch just worked.

Step 3. Place CC strand to the right (still at back), pick up MC strand under CC strand, make MC yarnover and knit CC stitch on the left needle with MC strand. Return MC stitch back to left needle, then pull CC strand to tighten the stitch just worked.

Repeat Steps 2-3 until desired number of stitches.
When working in the round, you may need to make an odd number of stitches and then pass the last knitted stitch over the first to join the cast-on.

The last photo shows reversed Kihnu Troi cast-on followed by one row of right-slanting Latvian braid. This effectively eliminates the twist caused by switching the yarns during the process (and also creates an illusion of regular Kihnu Troi cast-on ;)

Examples:
Sashiko Socks (second photo)
Secret Socks #4