I would be very upset about the explicit conversation. Becks and I have a very open relationship when it comes to things like online chatting or flirting in general. We can flirt a little with people we know as long as we tell each other that we did it. I know all of her online friends and most of her co-workers too. I have a female friend who I sometimes hang out with, but I always tell Becks all about any flirting that happened afterwards. We trust each other very much, but it does help to be open.
I am worried in your case because it is explicit talk. Also if she is doing this behind your back, that is a bad sign.