If it is a work supplied phone, expect zero privacy for anything you do on it.
I personally wouldn't surf any porn sites on a company owned smartphone/iPhone but that's just me.![]()
Did he say anything about surfing the web or did you just make that assumption.
If they don't have any VPN configured, and there is no iCloud backup setup to a work iCloud account, then I would say your application data is safe with you. As long as they don't make you hand the phone over to them.
Not sure what the all the other people are referring to regarding the employers ability to monitor what you do. Haven't seen any evidence to support that type of monitoring.....
If they have a MDM managing the device (I assume most decent sized companies do), then they can do much more than that. They can get a list of all installed apps. Check location (and location history), and a whole bunch of other info.