This has some interesting avenues for research. The likeliest explanation is that it comes from the X chromosome everyone has, which can get excited by female hormones. However, another known phenomenon (albeit rarely seen in modern society) is menstrual synchronization, where women living closely together tend to menstruate at the same time. This demonstrates some pheromone signalling across human individuals, so that may play a role in trans/HRT women having a menstrual-esque cycle. In addition to searching for causes, someone should really test whether treatments that alleviate misery for typically menstruating women (e.g. specialized pain pills, birth control pills, raspberry leaf tea, heaters, massage) also work for trans/HRT women. Figuring out the mechanism of quasi-menstruation would help, but effectiveness testing could be started before that to see if anything helps. Probably the mechanism would be needed to formulate a hormone therapy that would quash the symptoms if they are debilitating, which is another thing "birth control" pills are also used for.
More importantly, the current anecdotal evidence suggests there are things we should be doing:
* Make sure transwomen know that period-like cycles can happen to them and how to cope with the symptoms.
* Just as typically done with young women, also make sure they understand about the emotional ups and downs, how to work with instead of against those changes.
* Trans/HRT women may benefit from period trackers or other body/mind trackers to help understand their symptoms and reduce negative impacts.
* From a Pagan perspective, I wonder if having a cycle like that makes it easier to access women's magic, lunar magic, and/or menstrual magic. I've seen different reports as to whether or not transfolk and crones found those easy, challenging, or unreachable and now it occurs to me that those divergent experiences might -- or might not -- correlate to whether someone experiences a cycle. And causality for that could go either way. Looping back to how to reduce discomfort, though, I'd say if someone faces cyclic misery then magic is worth considering, because women have been using that solution forever and it works great for some.
* Don't assume, when talking to trans or HRT folks, that they aren't dealing with cyclic discomfort. Especially, don't badger them if they need to skip an event or take time off work because of it; they're miserable and embarrassed enough already just having to bring it up if they mention the exact cause at all.
* If someone has really rough cycles, treat it exactly as you would for anyone else with dysmenorrhea. Be gentle with them for the several days a month when they feel like crap, and try to schedule important activities at a better time.
* If you know about menstruation and are comfortable discussing it, and you see a transwoman friend struggling with those issues, you might discreetly offer yourself as a resource. Apparently this resource has a very small pool of people and most don't respond well.
* Somebody should probably start support groups for these issues, as they don't seem very compatible with typical women based on comments in the article. It might feel more comfortable for trans/HRT women to discuss this among themselves.
* In general, don't be a dick. Not only is it rude, it is riskier than usual rudeness because someone struggling with cyclic moodiness is much more likely to rip your head off -- especially if she doesn't have a lifetime of experience surfing those tides.
Do any of my audience members have this kind of issue? If so, what would help? Problems are best resolved by discussing them, and solutions may be shared across a group.