The employee working to get his hours works alongside the contracted NDE person and gets their hours. Most outside contractors will freely allow them to operate equipment, work on technique, sign log sheets to attest to hours, etc. Especially if it is part of their contract going into the arrangement.
Once hours are achieved they go to your company Level III, who may also be your contracted service provider, and test to get their Level II qualifications.
How much of the process do you understand? Are you aware there may be allowances for overlapping hours if they are going for two or more NDE disciplines at the same time? What spec in ASNT are you using? SNT-TC-1A or CP-189? Do you have a written QC policy for training and qualifying? Do you have a Level III on retainer?
Have a Great Day, Brent