Thanks everyone - the direction given in from Stig's post and Robot's video make more sense considering the engine's rotation. I even dug up an older service manual for a Kymco Xciting which was consistent with Stig's image, so I think I've got them installed correctly now.
As to root cause for the failed belt, I don't think it was rollers falling out of their track. Everything seemed to be in place when I removed that assembly. Well, that is until I popped open the ramp perhaps a bit too abruptly and rollers went everywhere... Also, the width of the still-intact portions of the belt that remained was only ~21mm, so whatever caused it appears to have happened over time.
Anyway, I did re-check clutch operation today in the garage and on a test ride - it still operates smoothly. The only other potential issues I could think of are:
1) Belt age. I still have the original packaging from that belt, and although it was installed on the scooter in 2018, the belt itself was manufacturered in 2013.
2) Riding style. Most of the miles on this belt were long-distance miles as opposed to just cruising around town or maybe the occasional 20~30 mile trip. One long trip was around 900+ miles stretched across 3 days. Another was the around 200+ miles. Of those 2 long trips, I pretty much cruised at a speed of 70mph or so.