It's dead horse time.
I would define cycling as any effect that takes cards out of your draw pile (without trashing them - i think that's an edge case that basically won't happen tho? dare I taunt the gods?). This includes chancellor, smithy, Fortune teller, rebuild, HP, etc. This article seems to be about sifting and not cycling. Chancellor and smithy both fall outside the "two meanings of cycling" described in the OP, so we know that something important has been left out.
(The main problem with my definition is that when you try to take cards out of an empty draw pile, then you trigger a reshuffle, so the net effect is to put cards into your draw pile. I don't think this is a fatal flaw.)
The salient differences between good and bad "cycling", as described in the OP, are to do with the effects of sifting, not cycling. As an article on sifting, it's fine, but it's confused because sometimes it really is talking about cycling.
The major mistake in the article is found in the statement that neutral cycling doesn't help you. Silverspawn identified the problem with here: it ignores the primary effect of cycling, which is to make the cards in the discard appear sooner.
Now, if we want to talk about how to tell whether cycling is good or bad for you, I think these are the essentials:
The value of cycling is determined by the relative quality of the cards in your discard pile vs the cards in the draw pile. If you're triggering a reshuffle, then you also have to consider the cards in hand and in play. So if you're building, then the cards in the draw pile are likely to be good, while the opposite is true for greening. Tracking what's in your draw pile will of course add information about what's in the draw pile and change the value of the cycling.
When cycling effects cause reshuffles, then the question of whether this is something you want is really more about reshuffling per se rather than cycling, but the same basic considerations apply: do I want these cards (draw pile + hand + in play) to miss the reshuffle or not? That is, are they relatively better or worse than the cards in the discard?
(PS: do not do a google image search for "picking at scabs")