There is most assuredly an art to flourishes and twirls that makes sure that nobody gets cranked. In our videos, we try hard to point out the more troublesome spots, or spots where someone might get cranked or put in an otherwise uncomfortable position since social dance is supposed to be fun, not painful, for all involved. This is also, incidentally, part of why we don't do dips on our videos. There are enough spots where those can go awry, and potentially with really serious consequences, that we prefer to teach those in person to folks who ask, where we can use spotters and ascertain in real time that our message -- especially the one about "if in doubt, leave it out" -- is understood.
Most important to all of these is the "ask" rather than the "tell" aspect...all contra flourishes are offers, whether made over the course of months of dancing with a particular partner or by explicit verbal asking or by more subtle "asks" -- for example, gently starting to raise an arm to twirl, or doing smaller flourishes to build up to larger ones like in waltz. It might even be working out the snags off to the side of the floor on a break, where they can be practiced at half-speed or whatnot until you build the muscle memory on how to lead the flourish smoothly or work on the timing for the lead-in with your practice partner or another.
The "answer" is the part where the partner accepts the offer and follows the lead to complete the flourish on time and then continues the dance.
The really key part of this, though, is the part where the pamphlet emphasizes that a refusal is just that, a refusal. That does not just apply to twirls, but to contra flourishes in general. And "a mature [dancer] does not take offense at this, as none, indeed, is intended."
A rather cynical part of me laments that most of the folks who need to get such a message won't go looking for it and thus won't find it (the pamphlet has been extant for 30 years now and it appears that the problem persists), but perhaps if we tell enough folks in the community, we can erode the issue a bit.