I think we need to keep Ephesians 6:12 in the back of our minds when we answer this. To my mind the two scriptures are referring to the same idea.
For we wrestle not against flesh and blood, but against
principalities, against powers, against the rulers of the darkness of
this world, against spiritual wickedness in high places.
Then 2 Corinthians 10:3-5 is saying that as spiritual beings we should war according to the spirit, not the flesh.
4 (For the weapons of our warfare are not carnal, but mighty through
God to the pulling down of strong holds;)
5 Casting down imaginations, and every high thing that exalteth itself
against the knowledge of God, and bringing into captivity every
thought to the obedience of Christ;
but then he adds a bit
And having in a readiness ( "and finally if necessary" is way is the way I read it) he's saying that when we have been obedient in this regard ( once your obedience is fulfilled) - or "as long as you've first done all that" - then we should always be ready to also carry the fight through to putting down disobedience should it come to that.
And having in a readiness to revenge all disobedience, when your
obedience is fulfilled.
To me this makes sense because going by the Ephesians scripture we're not dealing primarily with disobedience in either those around us or in ourselves, but rather spiritual wickedness in high places - but once the stronghold is pulled down - or once the strong man has been bound "Mark 3:27" then anything that remains is disobedience; which also needs to be dealt with.
I am not a Greek scholar but I suspect translating ἐκδικέω as revenge might be wrong. Surely it should be more along the lines of punish?