I don't think the question is whether it is/is not one's business, Gaia, but if one gets an email from one's T that has disturbing information in it, one has to "feel" about it and try to figure it out. If you accidentally get something in your email you think is for you and it turns out to be a note discussing "murder" (or "porn" or any other words that are triggers to you) you are going to feel/react, whether you want to or not.

I think one should talk to one's T about it but sometimes talking here first can make one feel more comfortable either talking to T about it or understanding where one might be thinking and concluding things that may/may not be true and help calm one down until one sees/can talk to T again.