Forgive me if I appear slow, as I'm unsure what you mean by "the TT becomes live" but, when the stylus is in contact with an LP, if you tap the TT base, wouldn't the induced vibration be transmitted through the disc and picked up by the stylus, but not when the stylus is not in contact with the record?
It happens this way with my RP3, so presumably the fault lies elsewhere? If vibrations are picked up/transmitted to the amp. when the tonearm is at rest, or raised from the armrest and platter, then you do have a problem, and as you've only changed the cartridge, was any stress placed on the cartridge wiring?
Have you tried swapping cartridges back to the original, to see what happens? Also, the new cartridge will need some running in, which may change it's sound.