You're confusing two different game concepts, which is understandable considering someone made the mistake of giving two completely different things very similar names.

Breaking it down:

1. The Race you choose has Racial Traits. You get all of these automatically, just like you're thinking of. You pick a dwarf? You get all the dwarf racial traits. The "Gaining Traits" thing you found has no relation to these.
2. Then the Advanced Player's Guide introduced a thing called the Trait system, which you can read about there. This is what the "Gaining Traits" thing applies to. These are optional mechanical bits you pick up for your characters. These traits are sorted into various lists, like Combat Traits and Equipment Traits. To confuse matters even further, one of these lists is also called Race Traits, which are so called because they always have a particular race for a prerequisite.

The racial traits from #1 have no relation at all to the traits system and race traits from #2.

The traits from the Trait system (#2) are like flavourful mini-feats you pick at character creation and which might reflect your character's personality or background (or you can ignore that bit). It lets you pick up neat features like an iron liver or an aptness at being a tactician. The Trait system is optional and your group can ignore it entirely.

The aasimar alternate racial trait scion of humanity can't grant access to human alternate racial traits

Up front: Don't confuse race traits with racial traits. Human (and aasimar) race traits are what the aasimar now qualifies for because of the alternate racial trait scion of humanity. On the other hand, racial traits are those specific facets of the creature's race that can be picked and traded for other facets of the creature's race because of the creature's race.

So, although the aasiamar has picked the alternate racial trait scion of humanity, the aasimar's race nonetheless remains aasiamar. Hence, an aasiamar that takes the alternate racial trait scion of humanity can no more pick human racial traits than a half-orc can pick human racial traits. An aasimar with the alternate racial trait scion of humanity could take as its two race traits Aspiring Bard and Bralani's Step, but the same aasimar couldn't take the human alternate racial traits heart of the sea and heroic.

So while the alternate racial trait scion of humanity says

Some aasimars' heavenly ancestry is extremely distant. An aasimar with this racial trait counts as an outsider (native) and a humanoid (human) for any effect related to race, including feat prerequisites and spells that affect humanoids. She can pass for human without using the Disguise skill. This racial trait replaces the Celestial language and alters the native subtype.

...this alternate racial trait doesn't give the aasimar anything the aasimar didn't already possess. Herolab shouldn't've allowed such an aasimar to pick the human alternate racial trait dual talent, first, because the aasimar's not a human, and, second, because the aasimar doesn't have the things the alternate racial trait dual talent needs to replace. That is, the alternate racial trait dual talent says that it

replaces the +2 bonus to any one ability score, the bonus feat, and the skilled traits.

And the aasimar, even if the GM allows the aasimar to take human alternate racial traits, doesn't have those other traits to trade away for this trait, making the aasimar ineligible for the new human trait, just as the aasimar would be ineligible for a feat that had as a prerequisite human and Str 70 (assuming the aasimar didn't have Str 70, obviously). Even were the aasimar to meet the human prerequisite—which it does—, it can't meet the remaining prerequisites.

Aasimar variants' ability score bonuses replace the typical aasimar ability score bonuses

That is, an aasimar gets either the typical ability score bonuses or the ability score bonuses for the variant he rolls or picks:

Players may choose one of the following six heritages for their aasimar characters in place of the traditional aasimar racial features. Each heritage presents new ability modifiers, spell-like abilities, and skill modifiers that replace the default aasimar racial traits, as well as a pair of custom traits. Each entry also discusses the most common (though by no means ubiquitous) personality traits, physical features, and places of origin of aasimars with that particular heritage.

Emphasis mine.