This GM would limit quickened attacks like a speed weapon
I suspect that the aegis astral suit customization quickened attacks is supposed to be incompatible with other effects that allow the creature to make additional attacks because the creature's just faster. (Hence the customization's name quickened attacks.)
Compare the description of the customization quickened attacks with the description of the spell haste that says, "This effect is not cumulative with similar effects, such as that provided by a speed weapon." And also compare the customization description with the description of the weapon special ability speed that says that it's "benefit is not cumulative with similar effects, such as a haste spell." My guess is that the benefit of the customization quickened attacks should've been phrased like those are rather than, for example, implicitly preventing the creature from employing the benefit of the feat Rapid Shot or denying the creature any attacks with an off-hand weapon.
Thus this DM would rule—despite the text saying that the customization quickened attacks "does not stack with other sources of extra attacks"—that it's the followup phrase "such as haste" that's more important in describing what the customization's benefit can be combined with, much like it is with the spell haste and the weapon special ability speed. (It is unfortunate that the customization's benefit is phrased so broadly, however.) (Whether a GM should forbid combining the benefits of the feat Rapid Shot with the benefits of the spell haste or a speed weapon is a topic for another question, but this GM sees that combination as legit, too.)
Nonetheless, a strict GM can limit the customization so that any source of extra attacks is obviated by the customization's benefit, in which case this player just wouldn't take the customization. That is, the customization requires the aegis to be level 10—therefore having a base attack bonus of +10 and 2 attacks due to that base attack bonus and a third coming online very shortly—, and the customization's benefit mandates the aegis to takes a full attack to realize it, so that instead of making 2 or more attacks—the first at his base attack bonus and the second and later at successive −5 penalties—, the strict GM says that the aegis has paid 3 customization points to make only 2 attacks—both at his base attack bonus. To me, this seems too high of a price to pay for a +5 to hit with a second attack that forces me to abandon all other sources of extra attacks. In such a campaign, I'd just take instead the customizations reach or burrow, those providing more versatility and greater strategic and tactical advantages than the literally-read version of the customization quickened attacks.