OP is correct, you are supposed to be able to apply Dex to Hit (Core 1) and to Damage (with Core 2) with Centered Weapons.
The issue appears to be exclusive to the Ninja Spy Attack/Damage Mod being applied. As the Henshin Mystic one (Wisdom Mod) correctly applies even to Esper the Shadowblade.
It might be that Ninja Spy Core 1 and 2 check to see if the Weapon is Centered already (or is checking a weapon type to add to it), and if not then applies the Dex to Hit (Core 1) and Damage (Core 2) then. But because all Shadowblades and Flameblades are Centered already, they don't get the Dex Mod to Hit/Damage. Unsure, but it is working differently from the Henshin Mystic version which applies for all Weapons whilst you remain Centered.
:: Edit : Confirmed Details ::
So it looks like it is something to do with the Short Sword weapon type itself, as it correctly applies to Mirana of the Flame (another Flame Blade). So with this test done, it shows that the issue is exclusive to Short Swords, otherwise the Dex Mod would not have shown up for Mirana.
Tests done:
Checked Ninja Spy Core 1 and 2 with Greatsword Kensai and got Dex Mod with Cores, none without. Checked staff that is Strength Only, gets Dex with, none without. Flameblades and Shadowblade weapons? Does not get it at any point.
Checked with Henshin Mystic 1 and 2 with Esper and got it Wis Mod active.
:: edit ::
To clarify, most Short Swords have already been modded to have Dex Mod to Attack and Damage so it's a bit redundant. So we can't really tell if it works or not. But the named shortswords (energy blades) that definitely do not use it (Shadow Blades or Flame Blades) fail.
:: edit again ::
As listed above now, it appears to be an issue exclusive to Short Swords, as other Weapons correctly get the Dex Mod from Ninja Spy Core 1 and 2.
J1NG