IT seems the employer needs to tell you if they spy/monitor your emails and this should extend if they spy on your screen or activity. If the worker is informed all should be fine then,it seems a very logical solution.
Edit I used the wrong email address in the past by mistake, it can happen if you have a few email addresses setup in Thunderbird and similar, after I done the mistake I made sure to double check the email address I used(I worked remote from my own PC).