Could relieving l3 & l4 nerve compression at l4-5 disc via mechanical traction therapy cause tingling in the penis/scrotum?

Traction : Traction can sometimes irritate nerve roots. Sounds like sacral nerve roots may be irritated.

Pudendal nerve: This nerve innervates the penis and scrotum and arises from the sacrum (s2-s4). It is feasible the lumbar traction irritated this nerve. Symptoms will likely be transient.

Traction effects: Not likely. Ask your chiropractor about common issues. Since there is no harness around your groin, this is unlikely. The traction if pulling through your legs/hips could actually stretch the sciatic and pudendal nerves. The latter supplies the scrotal and penile skin.