Concern of Prohibition After a Stain

Hello. My wife is taking pills that disrupt the hormonal system. As a result, the cycle came 50 days after the previous cycle and 20 days after stopping the pills. On the 50th day, she saw a stain in the bathroom that was permitted by a rabbi. A few hours later, intercourse took place, and a few hours after that, a small blood stain was found on the towel used for intercourse. A few hours later, it was found that she was menstruating. Does this mean that the menstruation started at the time of intercourse, and is atonement required for this? It should be noted that I am Haredi, and I do not need answers for those returning to faith. Thank you very much.

Shalom and blessings 

There is no clear evidence that the menstruation started at the time of intercourse. Unless the towel was used only by the husband. Or if the wife used the towel immediately after intercourse. 

However, if the wife used the towel after some time from intercourse, even if it was a delay of a few seconds, it should be assumed that the stain found on the towel appeared only after intercourse.

In general, the instruction of our teacher, the Gaon, Rabbi Ovadia Fried, in the case of a stain that does not prohibit, which appears at a time when there might be a vision, is to wait 24 hours [sometimes 12 hours, depending on the situation] before intercourse, to avoid prohibition. But in your case, according to the above details, there is no reason to fear that there was a prohibition. 

See Niddah 14 and Shulchan Aruch Yoreh De'ah, Siman 185