Hi, yeah that green definitely doesn't look normal. You said this is a newly installed green ink cart and B/G printhead? Are you sure they're legit HP products?
Like Paul said, just basic rolling back and forth to move ink from one end of cart to the other is enough. The ink is quite heavy and you can hear/feel it mixing.
If this really is a pigment mixing issue (don't recall ever seeing that before), it'll take a while for the mixed ink to push through the lines and head to give consistent output. You may notice some colour drifting until it stabilizes so you'll have to repeat cal/profiling/test prints to be sure.
You may want to burn some green ink on a green test print. Note it'll burn some other colour(s) too, since we can't tell the printer to just print one colour channel. But it should be less wasteful than the onboard "Purge Ink Plot" that does all the colours and cooks like 6 ft of paper.