I used the "My Tasks" filter which comes with the OOTB Task list. It shows older tasks which were created a few days ago, but in order to see the "new" tasks created within the past hour, I have to go to the "All Tasks" view and filter on my name. The only filter I have is "Assigned to = [Me]", so I'm not sure why it's excluding the others.
update: I checked the two items of mine which fail to show in the correct view, and they are somehow pointing to my name without the middle initial shown in my usual display name. Also, even though I receive the alert/email and can edit the task.. it doesn't count the account as my own. I have concatenated the list of approvers by email based on some fields I pick up (e.g., If price > 9999, approverstring = approverstring;[someHighLevelApprover]). I store all of those by email. Maybe I should switch them to user ID concatenations instead.