Uhh.. is it legit to just cut thru beams to put in piping? Over half of those beams are cut thru. I'd ask about that as well. I can't tell where this is, but if the plumber cut thru load bearing beams to put in plumbing that might be an expensive fix.
No, it's not. You can drill holes through the center of a joist or rafter but the permitted diameter of the hole depends on the overall width of the board. Notching the edge (or in this case cutting most of the way through it) dramatically weakens the board since the edges bear most of the tension from the load.
