I got my 12 yr old son to install a UN55 BB 122.5 mm spindle on a bike this morning. And simply, he did the following, as I instructed him:

a) look at BB shell and make sure threads are clean, surface looks flat and undamaged.
b) take out RH side cup/bearing/spindle and screw it by hand using left hand threaded into BB shell but not all the way.
c) take out LH side aluminum cup and screw it in by hand on the otherside.
d) take torque wrench and tighten RH side first to 35 - 40 ft-lbs torque. Get someone to help hold wrench and frame
e) torque LH side cup 30 - 35 ft-lbs as spec'd.

The first thing to notice is that when RH cup is not tightened, the LH cup may seem a bit loose inside and with some gentle finger grip it's possible to continue to hand-tighten both cups. This is normal. But once the RH side got torqued down tight, even I couldn't tighten the LH cup by hand anymore, even though we had 2 - 3 mm of threads remaining before the cup would bottom out against the bearing.

If you're tightening down the RH side snug, and then doing the LH side and the cup is loose, then it could be the wrong cup, and/or it could be something wring with your BB shell. But if a loose dry fit is showing the LH cup being a bit loose, I wouldn't claim it was a bad part yet until you've torqued it to spec, which is a pretty hefty 400 - 500 inch-lbs of torque (35 - 40 ft lbs.). After achieving that torque, then check if it's still loose.