The approach of trying to know what exactly the user does in their browser on their own computer and from that information to conclude whether something in front of the computer happened (the learning) is nonsensical at best and crime at worst (when done without consent or secretly).
Allow the user to give deliberate signals by marking parts as done and if necessary analyze the datetimes of those signals.
What expectations I have, is my own business. I definitely don't agree with being mistreated by an employer and it would probably make me look for another job, if an employer did that kind of thing.
'Expectation of privacy' is a legal term. It doesn't have much to do with your personal expectations.
In any case, what I meant is that actively lying and deceiving about whether you did the compliance training (or any other employer ordered training) can probably get you into hot water.