At work we can use wifi, but we have to log in with our windows login, so they can fully track what sites you go to, block porn, video games, etc...
I juse use the tor network and that 100% stops them.
Now for using a physical phone provided by a company, if you can verify or do a factory reset. If not, they could have like remote desktop, or spy programs on there like keyloggers.
If the phone can be shown to be clean, then you can safely use tor network and your company will not know of any sites you use, or data you use.
They will only know that you connect to tor network, read SMS, MMS, and incoming and outgoing phone numbers.