Hi - For reviewers who saw My Updates in Classic, the only thing they should see in Home is Approvals. Reviewers don't see tasks and issues in Home (only those with a Work or Plan license do). But you should double check that Approvals is checked off in the filter box.
Now there isn't a filter for document versus Proof approvals, but as you can see in my screenshot, if it is a proof, there is a label that states this one is a Proof approval.