The attack hits, but becomes a normal hit.
At the point where the effect of adamantine armor comes into play, the wearer has already been hit. Features and effects do what they say they do, and adamantine armor does not provide a way to convert a hit into a miss.
Improved Critical hits on a roll of 19.
The feature states that attack rolls of 19 hit.
...your weapon attacks score a critical hit on a roll of 19 or 20.
It happens to be a critical hit which has other implications, but the important part is a roll of 19 hits for a fighter with improved critical.
There's no mention of AC or other modifiers affecting this feature. It's a hit.
Adamantine armor removes the criticality from a hit.
Adamantine armor mitigates the subsequent implications of the criticality of the hit. Usually, this is the extra damage dice, but there are other features that operate on a critical hit which this armor also mitigates.
... any critical hit against you becomes a normal hit.
The armor converts a hit to a hit. There is no implication that a hit can be converted to a miss. A hit becomes a different kind of hit.
It's not by virtue of being critical that the attack hits.
Player's Handbook p.196 describes the impact of a critical hit which is to roll extra damage dice. Nothing about being a critical is guaranteeing the hit.
Rolling a 20 is what guarantees the hit.
The PHB section on Rolling 1 or 20 does not affect Improved Critical. The section (p.194) states a roll of 20 hits. It includes additional clarification to head off any confusion that might arise from trying to figure in attack modifiers or AC:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC.
It's a useful additional explanation to make it crystal clear, but the statement still stands. On a attack roll of 20, the attack hits. This is the same statement that improved critical makes about a roll of 19. On a roll of 19 the attack hits.
- Alice, a fighter with improved critical, attacks Bob with their longsword and rolls a 19.
- DM indicates this is a critical hit.
- Bob is wearing adamantine plate armor, which changes the hit from a critical one to a normal one.
- Alice rolls normal damage.
It's important to note at step 2 there was no AC calculation done. No checking the modifiers on the roll such as proficiency and strength. No need. Improved critical makes a roll of a 19 a hit.