Question Restatement
Why did the demons refer to Jesus as the "Holy One" -- and why would they have associated this with their "judgment"?
Alternative Answer
As an extra-biblical alternative to Psalms 16:10, Habbakuk 3:3, etc ...
References to the Messiah, as "the Holy One", can be found from the very beginning of the First Book of Enoch.
"Holy One/(s)" is used throughout this book, (chapter 25 and 37 esp.).
During that period of time, and in that culture, it was unmistakable as to what was being referred to.
CCEL, Enoch 1:3-5 -
Concerning the elect I said, and took up my parable concerning them: My Holy Great One will come forth from His dwelling, 4 And the eternal God will tread upon the earth, (even) on Mount Sinai, [And appear from His camp] And appear in the strength of His might from the heaven of heavens. 5 And all shall be smitten with fear And the Watchers shall quake, And great fear and trembling shall seize them unto the ends of the earth.
NOTE: CCEL, et al do not use "My", but rather "the" -- although "mou, (Greek Text)" is in the Greek. Either way, I cannot understate the translation questions with this book. Although its dating is certainly before Jesus -- the oldest manuscripts are in Ethiopic and Aramaic.
Enoch, Authenticity:
In order for the reply by the "demons" to make sense -- it has to meet fulfill three requirements: (1.) It has to reference "the holy one of God"; (2.) Has to be in reference to prophecy that predated Jesus; (3.) and it would have had to also prophesy their judgment.
Enoch fulfills all three requirements, (but just the first book of Enoch).
The first Book of Enoch was considered a very important part of Scripture, and cited even in the New Testament.
http://en.wikipedia.org/wiki/Book_of_Enoch
Because of this, when rereading Isaiah, etc, it raises the question whether "holy one" is actually a distinct identity in all of those passages -- though this would not be understood without the context of Enoch.
One of the translations of the First Book of Enoch
http://www.sacred-texts.com/bib/boe/boe004.htm