No, for normal network configurations they wouldn't show. It's most likely your system connmap is running on making those connections.

It's only showing connections directly initiated by your computer. Not anything "upstream" of you like the FIOS router. It would also show any connections TO your computer, but being behind NAT on a normal home network, that would likely be nothing unless you've intentionally punched holes.

You might be surprised how much traffic every device makes.