Yes , thats how i install them in my l&R locks.
It looks like you had a failure on that one strechman. From the wear on the top side it appears that it was installed correctly.
If the stirrup was turned the other way, the notches in the tumbler and spring would have to be deeper to allow full compression on full cock.
I had to replace a stirrup last year, can't remember what it was on but i had to make more clearance on the tumbler to get it to cycle properly without binding