Yes they should pop right after beating Shang Tsung or Shao Kahn.
So I ended up getting all the playthrough achievements and this is how I did it. Glitchy yes but they did pop for me.
I played MK1 on Normal.
Used both Sub-Zero and Scorpion. Used continues and didn't complete one test your might. Achievement popped
I played MK2 on Normal
. Used both Katana and Baraka. Used continues. Beat Shao Kahn and No achievement.
Got very angry
Played MK2 again on Very Easy
. Used Katana. Used continues. Beat Shao Kahn and the Achievement popped.
I played UMK3 on Normal. Played the novice tower
. Used Sub-Zero. Beat Shao Kahn and both the achievements popped for beating UMK3 and beating all arcade games.
So the only two things that stick out for me is that beating MK2 on normal didn't work yet beating it on very easy did.
Also people are saying UMK3 is not unlocking on very easy even though the achievement description says any difficulty which is why I did it on normal.