It appears to be counting the line "Added in 10.2.0" as an achievement to get, saying 15 out 19 instead of 15 out of 18.

Another example. Correct number should be 12/16

Uhhh... you've got something going on weird with your tooltips. ATT doesn't modify that portion of the tooltip, so another addon (likely something that works with achievements) seems to be taking ATT's tooltip additions and then adding it into the Achievement criteria itself.
For example here's my version of your first tooltip:

And here's my Waking Shores: Bronze dragonriding racing

So track down what addon is doing that, and tell them to stop being that way :P

Sure enough, only enabling ATT fixes it.

I tracked the culprit down to TipTacItemRef, part of TipTac. Thanks!