No they cannot see where you went on your home wifi.
Go to Preferences, Safari, and under privacy you will see "Private Browsing."
When this is turned on you can surf in peace as it leaves no trail. It's as if you weren't there. Be sure to go to the "Accept Cookies" box below it and set it for "Never" that way you are sure that your leaving no cookies.
Under those boxes you will see two that are "Clear Histor" and "Clear Cookies and Data." Click on them and choose "Clear" when asked.
The company now should have no record of what you did at home.
A really good IT department may get some hints from the fact that the History and Cookies are clean, but thats about all. A lot of people have "Private Browsing" turned on just so they can surf the web without picking up a lot of adverisements from where they've gone.
When I was looking for a new car I got a lot of junk coming my way from dealers I'd visited on line until I used private browsing. The I could look to my hearts content without getting pop up ads from Honest John or Crazy Al's Car Lot. 😀