How much monitoring is possible on a workplace-issued device?

1. I have a macbook air that is issued from an employer. When I first opened it, it had the usual setup screen (I assume that means nothing could be installed but the operating system?). There are no profiles in system preferences.
2. I also have an iPhone that has been issued from the same employer. It doesn't say it's "managed" in the settings.

Is the employer able to monitor these devices (specifically safari activity and messages) when I am not using their network?