This is a very interesting observation. I have been on Oestrogen now for over 3 years and about 5 months ago I started to get what appears to be impossible, a monthly cycle about once a month of period like symptoms. Typically they seem to last about 5 days. Interestingly when I transitioned before some 30 years ago and was living with my lesbian girlfriend when she got her period I also got similar symptoms.
For me, it starts with soreness and swelling of my breasts along with bouts of nausea in the morning just after I get up. The only thing that quells it is lots of water. Then over the next couple of days I generally get extreme and painful lower abdominal cramping that generally lasts a few minutes at a time. This is generally combined with nausea, as well as hot flashes, dizziness, and photosensitive headaches.
I also feel very bloated. Finally I get this terrible craving for chocolate. My cycle seems to lasts for about five or six days and it generally repeats roughly every 4-5 weeks, on a regular basis. I must admit as my body has feminized, the symptoms seems to be more prevalent, although since my GP increased my dosage recently, the effects have somewhat lowered in intensity. The doctor reckons that as my body is now relying totally on Oestrogen as its main hormone, the effects happen when my Oestrogen levels are down. Sort of my body telling me that I need to top up my reserves of Oestrogen.