I have Diablo III v.2.6.7 (not RoS yet), tried dozens of times but this events didn’t happen.
‘Cursed Mill’ and ‘Cursed Bellows’ can be achieved if ‘Cursed Shrine’ and special unique room in Hall of Agony L3 will be generated, and probably this is unavailable in vanilla D3.
And as far as I know these quests was added to D3 later.
Correct me if I’m wrong.
But ‘Cursed Cellar’ seems a regular quest and the only guess I have is that I’m too unlucky ):
I will appreciate for any help (:
The best way to get these Achievements is to play in Adventure Mode and fish for those particular Bounties. Unfortunately, you cannot do this since you need Reaper of Souls to access Adventure Mode.
The Events in D3 have been there since the game was released. (There may be some exceptions). But these Events are random. If certain Events spawn in your game, others will not. You’ll just have to “Leave Game” and “Resume Game” to farm certain areas again while looking for the correct Events to spawn.
Good luck and good hunting! 
Some updates:
Cursed shrines doesn’t exist in v.2.6.7.
I played a lot, watched latest uploaded videos and seems shrines was replaced with chests in all cursed event locations.
At Diablowiki website there is an information that Cursed Archive has shrine, but it has chest now!
https://www.youtube.com/watch?v=y8TlovPtc9E
Cursed Cellar.
After ~70 attempts few days ago I stopped and continue to play the campaign.
Today I tried again and with 3rd attempt I’ve finally found Cursed Cellar!
Since Diablo III is always changes with patches, I’ve uploaded video on youtube with specifying version and date.
https://www.youtube.com/watch?v=gzCQ51k9_g4
Also people feedback that Cursed Cellar is quite rare in this patch.
Cursed Mill.
Yes, it’s available * only * in Adventure Mode (RoS expansion is needed), and it is sucks if Blizzard did like that!
I’ve read ton of topics and seems noone in the world found it’s location in Campaign Mode.
Also youtube has no video evidence of existing this cursed chest.
Cursed Bellows.
Also doesn’t exists in v.2.6.7. People say that there was an XP exploit which was fixed in some patch, but it was * fixed * by completely removing this event from that game. Ha-ha!
Youtube also has no evidence of existence of this chest in latest patches.
You do know that Reaper of Souls is currently on sale for $9.99 USD through tomorrow, Monday, January 6, 2020?
I don’t know where you get your information from. But, I think you should find a new source.
It’s true, I cannot test this in D3 vanilla because I already have Reaper of Souls and I play in Adventure Mode.
Maybe this video I made between Season 18 and Season 19 will at least show you how I had to fish for The Cursed Mill Bounty and where it was located. (Randomly in Act I, The Fields of Misery).
Unfortunately, in Campaign Mode, you don’t have the luxury of fishing for the particular Bounty you need for a specific Event. So, I can understand how frustrating it must be to have to restart your Campaign game and hunt for an Event.
I took this screenshot, just now, with my Seasonal Demon Hunter in Season 19, Patch 2.6.7b. Again, I’m in Reaper of Souls, Adventure Mode. (I moused-over the Seasonal Buff icon to confirm this was Season 19, latest Patch. The Bounty Objective can be seen in the Objectives Window, under the mini-Map).
So, yes. These Events still exist… Even in the latest Patches. Continue hunting for them in D3 or purchase RoS and fish for them. Your choice.
Whatever you decide, good hunting. 
You may be right about this. I did some further testing and it appears that many, if not all, of the Cursed Shrine Events have been replaced with Cursed Chests.
When searching for information on Diablo Wiki, make sure you’re on Diablo Wiki | Fandom. Unfortunately, even though Diablo Wiki | Fandom has updated information, they appear to be currently in the process of updating for the latest D3 Patch. (Many of the Bounties listed are in red, indicating the pages do not yet exist).
It really shouldn’t matter whether the Event is a Cursed Shrine or a Cursed Chest. When you see either one, approach it. When you’re close enough, it will trigger the Event and the Objective will show under your mini-Map. If it’s not the one you want, try again.