If you looked at the link I provided, you'd see that there is not "a female hormone" that causes a period or symptoms - it's in fact a complex process of multiple hormones changing throughout the month.but, what is more probable is perhaps the human body, when it senses the ‘female’ hormone - prepares itself for that experience, thus giving every sensation of a period, but the actual bleeding.
I will however concede that it does seem entirely likely that the combination of oestrogen therapy and the placebo effect may result in a transwoman experiencing phantom pain or mood swings.