Ok, in the purest sense, the only way your work would see your activity would be if you were doing said things within that virtual console. Just like if you were at work.
The unknown aspect would be what they installed and what you agreed to when you installed it.
As a "for instance", my son was in University. In order to be able to connect to the internet at school as well as to be able to do work and take tests from home, he had to agree to install a host of hardware and token that allowed the school to see exactly what he was doing. It would even go so far as not to allow unauthorized pages from opening on the machine he was connected to school with. It had no way to see other machines on our LAN/WAN so if he wanted to "cheat" he just had to use another device like a phone, tablet, PC, etc.
So, in the simplest terms they shouldn't be able to see what you do outside that virtual environment, but would be specific to what you agreed to and installed. My suggestion would be that if you value your job and yet still want to screw around some like many people do...it would be safest to do so from another machine such that there is no way for them to be seeing it from your internet service.