Based on the text put on my package, I assumed that the review would happen automatically. But now I'm seeing some packages that were added after I submitted mine be accepted. Do I need to perform some action to initiate the review?
Hi, you don't need to do anything but click the "Submit for Review" button - which you did. Commenting to bump it does help, though.
It tends to be easier to review packages by authors who have been creating for longer, often only requiring a once-over of the package page. With newer users, we tend to need to check the contents to look for mistakes like licensing and such.
The author of the package also messaged a link to their mod in a chat room, which prompted me to check and approve it - skipping the queue :P