I had a ongoing ticket made in game and was recently told by a GM to take it to the forums and make it a bug report. i figured out how to post links. So heres the ticket response: https://imgur.com/a/HRHvFk3
But anyways i will get into the issue. For the mount parade achievement the progress tracker has not gone up by 4 when i crafted personally and added the 4 gem crafting panthers to my collection. I crafted them and added them to my collection on this character.
As per the GMs request, i have logged onto all my characters and the number has stayed the same except for when i logged into the paladin. it went up by 1,(the paladin is level 27) not by 4. As the GM’s confirmation profession mounts DO count towards the achievement.
I recently got Midnight’s Eternal Reins from new karazhan on Tuesday, and that one worked, it went up by 1 on the progress tracker for the achieve. But for some reason the panthers did not progress the achieve by 4 (or assuming that 1 it went up by was one of the panthers 3 more).
I logged into ALL of my characters with the achieve progress tracked. and took screenshots for each. theres to link for you to see for your self: https://imgur.com/a/FfNnmW1
i got the Witherbark Direwing last night (One of the arathi rare mounts) and the count originally didnt budge from 194 but upon making a trial 110 pally it went up by 1, and went up to 195. So i am still missing the 4 counts on the achievement. (3 perhaps if that one was a panther before, like i was talking about)
TL;DR
I made the 4 gem crafting panthers, they didnt progress my mount collection achieve, made a ticket was told by GM to log in all of characters and if that didnt work make a bug report.
There’s definitely some funny math going on.
My Warlock -should- have more mounts than my Paladin (my warlock has all the class mounts, my paladin does not).
But I didn’t get Mount Parade until after I logged into my Paladin anyway. I’m at 354/400 mounts towards “A Horde of Hoofbeats” now, but the mount journal claims I have 402 mounts. And under the [statistic] tab of the achievement journal it says I have 352 mounts (not 354).
So, I don’t know what to tell you. Try mounting up on each of the mounts you crafted while on your Paladin and see if that shakes something loose? 
Rode all 4 panthers for a good 10-15 seconds each, and i did this on the Warlock, (One who crafted them) the 27 paladin, and the 110 trial paladin.
Nothing changed 
The mount achievement is tracked by the single character that can use the most mounts.
The most likely character is the one with access to the class specific mounts (Death Knight, Paladin, etc) or profession based ones (Tailor, Engineer, etc).
The screenshots of the achievement really do not help, What is needed is for you to look at the Mount Journal of each character.
Well yes, i know it is tracked by a single character. i had this same exact discussion with the GM.
But why didnt the achieve go up by 4? The mounts although being a profession mount are useable by every race and class. reguardless of profession, i can even use them on characters that have no profession. That being said they appear in the mount journal of EVERY character. So wouldnt it only make sense for the achieve to progress by 4?
How do you know it did not go up by 4?
Did you have another Paladin or other profession character that you deleted? Or changed professions?
As to the profession mounts, it depends on the mounts.
The jewelcrafting mounts should be useable by all.
But there are the flying carpets only useable by tailors of the appropriate level. There are engineering mounts that can be used by all, but there are some engineering mounts that can only be used by appropriate level engineers.
You have to check each mount to see which can not be used by that character. Unfortunately, rather tedious and time intensive work.
Because i tracked before and after i added the mounts?
Midnight got me to 193 (That was tuesday) so that was days ago
Logging into the paladin got me to 194 (I dont know why)
I crafted the panthers and added them into my collection before i logged into my paladin that got me to 194.
So you see thats how i know it didnt increase.
Okay, it was (excuse my language) tedious to read your original post, because you repeated things even before you got to the TLDR.
Also, I just checked some things.
In the Mounts journal, the Total Mounts at the top is the number all mounts collected. What is shown in the scroll box below that is the mounts that character can use. So it will not show Class- or Profession-specific mounts.
So what you can do is scroll through that for each character and count the number of mounts that are highlighted (not grayed out).
That is the best way to verify and set your mind at ease. (Sorry, I do believe the achievement is tracking correctly.)
I actually went through and counted all the mounts in my statistics on the character that is registering that i have 195 mounts on. and manually counting im at 185.
so im uh lost
edit: the mount journal claims i have 238
Check each character on the account.
Did you delete a character or change professions?
Have not changed professions recently. the only one i can remember is at the beginning of BFA i changed herbalism to leatherworking on my DH. I deleted some trial characters. thats about it.
How to find out your character mount count? I am glad you asked.
Achievements -> Statistics (tab) -> Character -> Gear = Mounts owned.
I’m having a similar issue. I have over 231 mounts on multiple characters that show in the mount collections tab. I submitted a ticket, the GM said to post it on the forums.
The achievement progress shows I have 194 mounts.