OS X management profiles / root certificate
MDM (Mobile Device Management) profiles can change many settings within the system. As you suspected, in this case the software update mechanism was redirected to a company server. There were likely other settings as well. If the profile forced all network traffic through a VPN, then the company could view it in transit. You can check by looking in the network preferences for interfaces labeled "VPN" in the interface list. 

Since you deleted the profile, you should be ok. Check the network settings, and also look for applications that may have been installed by the profile in /Applications. One other thing to look for, would be CA certificates installed into either the System Roots or the System Keychain. Use Keychain Access and search in the System Roots for anything including the name of the company. Do the same for the System Keychain.