When tags on a post are saved to the database, they are sorted in the following order:
- Required
- Moderator
- By number of posts (
desc
) using the tag
The sort order of the tags is determined at the time that the tags are saved. This is not calculated when the post is displayed - it takes the saved sort order.
The current posts that use product-discovery are:

You will notice that only one of these posts has the tag showing up in its proper place (second). So why is that?
It has to do with the timing around these posts. They were all posted on April 23, between 16:27 and 18:11.
However, looking at the history of the tag, the product-discovery tag itself was not actually made into a moderator tag until April 24 at 13:34 (I know, because I ran the dev route to do so, check out the tag wiki history as well). So since at the time that these posts were made, and tags were saved for the first time, product-discovery was not a moderator tag, it was sorted to the end of the list (since it had the lower post count of any of the non-required and non-mod tags that were added).
So why does one of the posts have the tag in the correct position (second)? Because that post had its tags edited after the tag was made into a moderator tag. The tag edit happened on May 7, when I removed the featured tag:

You can see here that the product-discovery tag actually switches position from last to second - the resorting will happen whenever tags are edited.
Hope that this has cleared up the mystery.
out of place mod tag
has Glorfindel stumped, for real
timing is the key