Indeed. The rule Hastiator quotes prevents an ability like Vader's or TRC's from producing both the card effect and the usual token effect when spending it.
If Admonition required spending of the token (which, as pointed out above, it doesn't) another, more fundamental rule would kick in:
RRG p.4, Defense Tokens:
A defense token cannot be spent more than once during an attack.
So you could not spend a readied (green) defense token for its usual effect, then spend it again with Admonition (triggering a discard because it was already exhausted), because that would be spending it twice.
However, Admonition requires discarding of the token, which:
1) does not constitute a "spending", so the rule quoted by me does not kick in
2) does not produce any "normal" effect, so the rule quoted by Hastiator does not kick in
What's happening here are two separate, unrelated events:
i) A token is being spent by the defender for its normal effect
ii) A token is being discarded by Admonition for that card's special effect
The above tokens may or may not be the same one. None of the rules quoted so far prevent the same token from being chosen, because the conditions simply aren't met.
adding to the above quote... remember you could essentially use Admonition on a GREEN defense token to "discard" it and get the ability of the Admonition card, not that you would ever want to except in extreme cases. I think me stating that further defines that you "discard" a defense token at any time regardless if it is GREEN or RED to gain the effect of Admonition.
simply put, you "spend" a defense token to turn it RED, you "spend" it again to use it then it is "discarded".
with Admonition the word "spend" is never brought up, you just "discard" it, therefore the rule.