The patch transfers estrogen *through* the adhesive - the adhesive actually is doing double duty as the suspension medium for the medication. What that means, basically, is that there is no way for estrogen to be administered from the top/non-sticky part of the patch, and furthermore that if you were sweating enough to actually share any estrogen with her you'd also have sweated enough to make the patch fall off completely.
With that said, my wife had issues with her period getting wonky when I went off my HRT for surgery, and at that point obviously there was nothing at work but my native hormones. Her best guess is that it's the same mechanism that allows women to "sync up" when they live together; whether that's pheromones or what, it's a documented phenomenon and it makes sense that it'd be possible to be caused by trans women who are living with estrogen-dominant systems as well.
Or it could be coincidence. Periods are weird, and it's tempting to blame something for them going wrong.