Safety Knights

According to the standard, at the time of initial assignment.

To me, that's before they conducting any task that may result in an exposure.

I cannot speak to NCOSHA only Fed. Tim, is correct training must be prior to exposure 29 CFR 1910.1030(g)(2)(II)(A). Since any employee can be exposed to OPIM (Other Potentially Infectious Materials) at anytime, from other employees, this means "Affected Employee Training" which is everyone, should be at NHO (New Hire Orientation). Affected Employee Training is simple, "Unless you are fully trained in Bloodborne Pathogens, an Authorized BbP employee, and approved by Management, You DO NOT TOUCH OPIMs AT ANYTIME!" As an Old Personnel/HR Manager as well as the "Safety Guy" for over 45 years that is required. Since NC must comply with OSHA first, it must be at least say that, but maybe more stringent. I have worked on Temp assignments in Greensboro but just not that familiar with NCOSHA.
I also think all this means employees must be trained as "Authorized Users" before they can work around and with OPIMs. As OSHA says "Occupationally Exposed".
In training I borrow the terms "Affected and Authorized" in a lot of my OHS Training, borrowed from 1910.147 and possibly other areas. I think it illustrates the difference in employees that that must have general knowledge to those other employees that actually must use those competencies to keep themselves safe. An employee that sees a PFP harness and knows what it is, and knows they cannot don it is "Affected". The employee that does don the harness, and received current training on the competencies to safely wear it, is an "Authorized User of Personal Fall Protection".
My $.04!