This answer has been edited to reflect recent guidance on Twinned Spell. This answer originally was: "You can twin the spell as long as you don't target an object."
Your first interpretation is correct, with some technicality.
RAW and RAI, the spell needs to target exactly one creature and cannot be capable of targeting anything else - including objects - in order for Twinned Spell to work.
As you've noted, the Twinned Spell metamagic option begins its description with:
When you cast a spell that targets only one creature...
A 2015 errata to the PHB added this note to the description of the Twinned Spell metamagic option:
To be eligible for Twinned Spell, a spell must be incapable of targeting more than one creature at the spell’s current level.
This means that a spell like Chaos Bolt, though it does initially target only one creature, is ineligible to be twinned because it can target more than one creature.
Further, as you point out, spells - like Fireball - that instead target points in space are also ineligible to be twinned. (More on Fireball later)
Nystul's Magic Aura, on the other hand, while it does only target one creature, can also target an object.
Apparently, according to recommended guidance in a 2020 version of the Sage Advice Compendium, spells that can target objects are ineligible to be twinned:
If you ... are still unsure whether a particular spell qualifies for Twinned Spell, consult with your DM, who has the final say. If the two of you are curious about our design intent, here is the list of things that disqualify a spell for us:
- The spell has a range of self.
- The spell can target an object.
-- Sage Advice Compendium, page 6
According to this guidance, Nystul's Magic Aura cannot be twinned because it can target an object, and that's that.
But I personally think that's a bit dumb.
This DM has allowed - and will continue to allow - spells like Fire Bolt to be twinned. I interpret the rules to mean that if you target a creature with a spell, you could then twin the spell and choose a new creature to also be affected; but if you choose an object as your original target, you could not then twin that spell.
An aside about targeting and that podcast:
As of January, 2019, Jeremy Crawford's - or any other staff, for that matter - public statements are no longer considered official rulings. Only the Sage Advice Compendium is considered official as far as rulings go. Many of the past statements regarding rules clarifications have been published in the SAC, but many have also been excluded (or just haven't been published yet). This means we can only rely on what is published in the SAC, and we should throw out all previous rulings in tweets, podcasts, etc.
I searched the SAC, and unless I missed something, the SAC does not currently appear to define anything in regard to spells automatically targeting things they affect. Where there might be exceptions, they seem to be explicitly covered in the description for a given spell. Fireball is actually one such spell. It initially targets a point in space and then treats the affected creatures like targets (emphasis mine):
Each creature in a ... sphere ... must make a Dexterity saving throw. A target takes 8d6 fire damage...
However, like I mentioned, this is explicitly phrased in the spell description, and not an assumption we make because the spell affected additional things. "Affect" does not automatically translate to "target" unless the rules for a spell say it does.
Nystul's Magic Aura targets one creature or object and affects them the way the spell describes (emphasis mine):
The target can be a willing creature or an object...
"The target" in this case is explicitly defined. Later, if another spell targets the same target, Nystul's defines how that other spell behaves. That is the extent of the interaction. We choose Nystul's targets when we cast the spell. We do not suddenly have additional targets when someone else targets our target. Nystul's does not mention the other spells becoming targets, so we cannot consider them to so be.
Jeremey Crawford's ruling on Dragon's Breath directly contradicts the reasoning of the 2015 PHB errata. Dragon's Breath targets "one willing creature" and that's it. Later, regarding the breath attack, it says (emphasis mine):
Each creature in that area must make a Dexterity saving throw...
Note that unlike Fireball, this spell does not declare the affected creatures to be targets. The fact that the breath attack granted by the spell can affect multiple creatures does not change the fact that the spell only targets one creature. This means that Dragon's Breath is, in fact, an eligible target for the Twinned Spell metamagic option.
The confusion caused by Jeremy Crawford's initial Dragon's Breath ruling is a great example of why the decision was made to retcon all rulings from before 2019, leaving the Sage Advice Compendium as the sole source of official rulings going forward.