My work PC computer(in my home office) is connected to my home router via ethernet cable and I'm connected to my company server through VPN (NetExtender). If I'm logged onto the remote terminal server on my work PC and I have my personal macbook connected wirelessly through the same router, can they track my internet usage on my personal macbook because they are using the same router?
They generally won't be able to track your non-routable internal addresses(often 192.168.x.x), but of course, they can track your routable external IP address (the one your ISP gives you). The IP on you macbook should be safe since it is not connecting to their VPN, and getting an internal IP address from them.
Even as in that comment to the question that Moab posted, if they did force Internet browsing or other services through their VPN, the IP address the VPN would give you on their network would be recorded, and even that is not the case with you RDP'ing since all the work would be done on the Terminal Server.