Havoc Demon Hunter stat priority is apparently (according to wowhead): Ag/Crit/Mast/Haste/Versa (both trees) and AMR is using Ag/Crit/Haste/Mast/Versa (both trees). Both Crit+Haste appear to have the same priority and Mast/Versa seem also very close. I will manually set it for now and see how that works out. Once again I apologise that I caused offense to you.
According to who…? Blizzard?
If you’re new here, know that the coders do not work on strict priorities the way all other sites do; if you can guarantee what gear you get & when, then you can stick to a hard priority.
AMR’s optimiser factors all secondaries at the same time & works to get the best throughput from your available items.
Asking for clarification of why a system works the way it does is fine; categorically telling the site coders they are wrong… if not outright rude.
I am so sorry that my choice of language offended. Please accept my apology. I have updated the original post hopefully to your satisfaction.
It’s difficult to give a “one size fits all” stat priority – I would need to see your specific character to comment. Press the green “help” link next to the big Best in Bags section header on the website, and copy the generated 32-digit code here. Then I can see your specific character, available gear, talents, etc.
Just noticed your response - thank-you! I will do as you suggest later on tonight as I have a RL thing I must do right now. Thanks for your rapid response! 
Here is my Havoc DH build:
afd836c4ecd0423ca3dc0c35272ec336
Crit=621 Haste=671 Mast=259 Versa=318
I did force the Algeth’ar Puzzle Box (which boosts Mastery) against the advice of AMR and I didn’t want the 2-set to be broken either (I have since found the Force Tier checkbox though). Unlocking the Puzzle Box for what AMR chose instead made no difference to the overall stat spread. I understand that your way of selecting gear allowing the excellent and unique feature of gear-from-inventory selection while requiring far less brute-force computation will from time to time produce (what at first look like) outliers and so I thought this example might be worth bringing to your attention. Thank-you!
You have no talents selected in that setup. Choose one of the auto-update options under Step 1 of the Set Up Best in Bags tab, or manually choose the talents that you want to use, then try optimizing again – do the results look more like what you expect? If not you can post another snapshot here.
e1c17e0afd104f7db226d7f81a1fe730
This time I made sure my Raid Low Mover talents were selected and I also deleted all my custom setups (as a precaution) and let AMR choose whatever gear it wanted (although I did force the tier set using the checkbox).
Crit=638 Haste=683 Mast=259 Versa=333
Sadly, despite my error (sorry about that), the stat priority appears unchanged from before.
There are still no talents selected in that snapshot…
If I put in a fel-scarred build with just Initiative (which is what I assume you mean by a “low mover” build, but maybe you are playing aldrachi reaver… either way it won’t matter that much), it picks the gear that I would expect: high crit and mastery, and it gets the set bonus as you would expect without having to force it, and it also chooses the puzzle box by default.
Let’s figure out why your talents are not getting loaded… start by doing the following: choose the option in this screenshot below, then press Find Best in Bags which will ensure the option gets saved to the server:
Then go in-game, and make sure that you have the talents active that you want to use. Then export from our in-game addon to the website using the export tab of the addon and pasting into the import from addon box on the site:
When you do that, it should automatically populate your talents now that you have the “Last seen talents for this spec” option enabled on your Havoc Best in Bags setup.
If you optimize again, you should see a better result now that you have talents.
It’s fixed now and you’re right - it was all my fault. I haven’t updated my AMR addon since January 18th (ie pre-expansion) and that was the root cause. Let me take this opportunity to thank you for your patience and diplomacy as well as your thoughtful responses. I really appreciate the effort that you have put into this and I am sincerely sorry for wasting your time!
No problem, I’m glad we got the site working for you!