I am 20+ years removed from my minilab experience but the problem here is at least two-fold. First is under exposure. If that were the only issue, the black would still be BLACK, not some other hue. If we assume that the other part of the problem is film processing... it’s obvious there is serious crossover happening with the RGB plots, particularly in the shadows. If the lab’s process was in balance, i.e. tested daily and adjusted accordingly (read: replenishment within manufacturers specs), the plots would remain consistent right to the bottom of the toe. Easy-Peasy, but you have to monitor daily. The negatives look overly magenta to me, which is consistent with the green print cast.
The other side to this is the scanning, as has already been mentioned. OP when you scan your negs turn off all adjustments in your software. Be sure you are scanning just the full negative area, including the shadows, but don’t compensate in the brightness/contrast, curves, levels, color balance or any other setting. Turn off all automatic controls. Once you are sure of that, than your resultant scan should accurately reflect the information within the negative. If your scan returns the green cast in the positive, or magenta in the negative—your scanning is probably accurate and as good as can be done in this instance. The problem is somewhere in the processing.
Any properly exposed negative with the full range of tones and the magenta cast would be harder to spot as the printing machine would have enough information to correct for the cast. The problem could be on the printing side of the operation but given how the negatives look to me, I think it is the film development.