As much as I am loathe to say it, this is a DM discretion call. First, some questions because the answers form the basis for how to handle anything other than a natural 20 against normal armor.
What is a "critical hit"? What is an "automatic hit"?
There are three relevant places critical hits come up: the general combat rules regarding natural 20s, the specific rules for adamantine armor, and the specific rules for champion fighter. Taken individually or in pairs, these three references to critical hits may seem clear. Considering all three together creates a situation where the ruling on one pair affects the ruling on the other.
Here's the can of worms...
The Basic Rules have the following passage:
Rolling 1 or 20. [...]If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, which is explained later in this section.
Later on in the Damage Rolls section, it describes the damage effects of a critical hit. It all seems clear at this point - a natural 20 being automatic hit and a critical hit are the same thing.
However, when we look at the champion fighter's Improved Critical ability, we have:
Improved Critical. Beginning when you choose this archetype at 3rd level, your weapon attacks score a critical hit on a roll of 19 or 20.
"Rolling 1 or 20" indicates that a die roll of 20 automatically hits, and calls it a critical hit. Champion fighter also calls a 19 or 20 a critical hit. Does that mean a 19 is also an automatic hit just like a 20?
Adamantine Armor says:
While you're wearing it, any critical hit against you becomes a normal hit.
What's a "normal hit", then? Remember that Armor Class is not about being hit, it...
...represents how well your character avoids being wounded in battle.
A "normal hit" uses the comparison between attack roll and AC to determine if the character is wounded. When an attack roll doesn't match the target's AC, it doesn't mean the attack misssed, it just means it didn't hit well enough to do damage.
There are two choices, both logically sound, each internally consistent, but also mutually exclusive.
- If the DM wishes to consider an "automatic hit" and the dice-doubling "critical hit" to be separate things.
- On a 20, adamantine stops the damage ("critical hit"), but the "automatic hit" carries through because a 20 always hits.
- Champion fighters automatically hit on 20s, but not 19s (a 19 is a "critical hit" but not an "automatic hit".).
- If the DM wishes to consider "automatic hit" and the dice-doubling "critical hit" as synonymous:
- Adamantine stops the dice-doubling from the "critical hit" and, because they're the same thing, also stops the "automatic hit" (compare the total attack roll to the AC as with a "normal hit").
- Champion fighters count 19s (and eventually 18s) as "critical hits", which means they are also "automatic hits".
To put it differently... any two of them (the combat rules, adamantine armor, and the champion fighter), isolated from the third, doesn't leave much room for doubt. It is the interaction of all three passages that creates ambiguity.
I've specifically avoided sharing my opinion, and presented two possible interpretations. The published rules don't provide sufficient clarity or weight to make an iron-clad determination either way.
On Twitter, "official" rulings, and designer intent:
While there are some designer-intent posts on Twitter, they have not made it into an officially published errata. Considering the number of times those seemingly official posts have made a call then reverted it, they should all be considered suspect. In fact, in the time since this answer was originally written, WotC has issued a new edition of the Sage Advice Compendium indicating that live tweets are not official clarifications until they appear in a published SAC.