The cat does not need to be glowing to work.
Visible smoke would indeed persist longer (distances from the cap) than steam. Steam can sometimes appear a foot or so outside the (shimmering) cap, or it can appear from right inside the cap, but (in my case) it disappears within 6 ft - rather than slowly dilutes as smoke would do.
Smoke, even from a working cat, depends on the residence time of the exhaust gases in the cat. The longer they are there, the more complete the combustion will be. And the hotter the cat the more complete the combustion will be.
So if you open the Tstat, what you are doing is almost instantaneously increase the airflow = decrease the residence time. So combustion will be less complete. After a while, the cat has seen more fuel (because larger air flow, assuming the primary combustion efficiency is not changing, see below), and will get hotter. At that point, the combustion gets more complete again, and smoke may disappear.
Regarding primary combustion: if one opens the air flow, a new steady state will eventually appear where more fuel is combusted in the primary fire, and that can result in less fuel for the cat, so it may cool down again. This may h appen for larger Tstat adjustments. For smaller ones, I think the above assumption of similar primary efficiency is fair.
However, a cat cooling down will less likely give smoke because it's exhaust-combusting capabilities are high (because of the high temperature) for the amount of fuel it is given.