It's a new faucet in a new sink. I haven't torqued the tubing
yet, but maybe I was too careful. It doesn't leak when the faucet
is turned off, but when I turn on the water into the sink, it
starts spraying from the 1/4 inch connector tube, a one-foot
metallic tube than joins two small copper tubes coming out of the
control valve (one metal gizmo that controls flow and hot/cold).

I'm guessing it's a compression fitting. You should not have to
hold the
tube , if the fitting is two pieces you should be able to get a
wrench on each half and then tighten. Do not let the tube spin or
it will twist and crimp. I can't see it to know for sure.

I could grip the tube itself with a robogrip pliers, I suppose, but
it's not a good grip. The tube doesn't offer anything better on the
top side of the connection. It will twist and crimp, I don't doubt,
if I get too strong with it. But too weak and it leaks. That's why I
am thinking I bought a turkey sink, and should just get another one
with proper 1/2 inch connectors for hot and cold.