Can the Tech Support of Microsoft see what I am doing while I chat with them???

Hi guys.

I am a bit shocked.
Either I have just experienced one of those absurd coincidence which (should) have very few chances to happen, or I was spied by Microsoft while chatting with them (and Comodo could not prevent it).

I have contacted the Microsoft Tech Support (the free one) via chat.
At some point the guy said “super, it seems you are watching one piece the anime?”.
I was paralysed. I actually really had the last chapter of One Piece open in another tab (although it was the manga, not the anime).
I have immediately closed firefox because I was writing private personal things to a friend while waiting for the answers of the Microsoft guy, and I demanded him to tell me exactly how he knew what I was watching.
He said “there is a character in one Piece who say Super all the time, like you do”.

Now, I say super because I live in Germany since a few years and here everybody says super. I just got used.
So, “super” is surely not a trademark of One Piece, and in fact I could not even think to which character of One Piece says super. I have never paid attention to that.

How many chances there are, that while I have one piece open in firefox, and I am chatting with Microsoft on another firefox window, I meet a Support guy ho knows One Piece, and who (like very few people do) breaks the formal protocol of the chat asking something personal, choosing the wrong words (he did not say “do you by chance know One Piece? I wonder if you say super because of the one piece character who says super”. He said “it seems you ARE WATCHING one piece”, like, watching NOW), and all just because I say super, which is not necessarily a one piece thing?

I mean… Seriously!?

Can it be that the guy, just having the chat open, can install some kind of hook, of whatever, and see what I am doing in the browser I use to chat with him?

When I read Free Microsoft Tech support then I get suspicious. How did you get in contact with them? Through what website?

Nah, it was directly from Microsoft. I mean, it was the official free Tech Service of Microsoft. I was on Microsoft’s website, clicked on support, selected “technical”, etc.
When I say free it is because the first (copy and paste, template) thing the guy wrote was “please note, you are going to receive the free support. If your request needs a complex solution, you may prefer to contact the paid support”. And I think there was the link for the paid one.
It is a way to say “we are just normal guys like you who pay the bills by working in a third party call center and we do not have a real technical preparation”.
I worked in a call center too, which at that time had a contract with Microsoft, and I worked at first in a sector to give “support” for the upgrade to Win 7 (or was it Vista?). When people needed technical support we had to derive to real Microsoft Technicians.
So it must have been something similar.