What "Paul" is trying to impress on Timothy is that the message that H&P were spreading around was not only incorrect but also subversive:
ESV 2Ti 2:14 Remind them of these things, and charge them before God
not to quarrel about words, which does no good, but only ruins the
hearers. 2Ti 2:15 Do your best to present yourself to God as one
approved, a worker who has no need to be ashamed, rightly handling the
word of truth. 2Ti 2:16 But avoid irreverent babble, for it will
lead people into more and more ungodliness, 2Ti 2:17 and their
talk will spread like gangrene. Among them are Hymenaeus and
Philetus, 2Ti 2:18 who have swerved from the truth, saying that the
resurrection has already happened. They are upsetting the faith of
some.
The author implies that the teaching of H&P saps the Message of its moral imperative to holy living. He draws analogies to professions that require great patience and diligence for success:
2Ti 2:5 An athlete is not crowned unless he competes according to the
rules. 2Ti 2:6 It is the hard-working farmer who ought to have the
first share of the crops. 2Ti 2:7 Think over what I say, for the
Lord will give you understanding in everything.
He urges Tim to consider the fact that Jesus, even though he was God's anointed and the rightful heir of David's throne obtained that throne through obedience to God all the way to death:
2Ti 2:8 Remember Jesus Christ, risen from the dead, the offspring of
David, as preached in my gospel,
And he points to himself as an example of suffering in order to obtain a goal:
2Ti 2:9a for which I am suffering, bound with chains as a criminal.
2Ti 2:9b But the word of God is not bound! 2Ti 2:10 Therefore I
endure everything for the sake of the elect, [in order] that they also may obtain the salvation that is in Christ Jesus with
eternal glory.
He then draws out a universal principle in a catchy saying applicable to all, ala "No cross, no crown":
2Ti 2:11 The saying is trustworthy, for: If we have died with him, we
will also live with him; 2Ti 2:12 if we endure, we will also reign
with him; if we deny him, he also will deny us; 2Ti 2:13 if we are
faithless, he remains faithful— for he cannot deny himself.
It is in this context that he vilifies the message of H&P which stands in stark contrast. Given the juxtaposition of Paul's message against H&P's one can infer that H&P taught that the salvation of the believer was a "fait accompli", a "done deal" and was not bought with one's own blood, sweat and tears. This is, of course the message of much of modern Evangelicalism and in particular, Calvinism. A parallel to the current polemic is found here:
1Co 9:23 I do it all for the sake of the gospel, that I may share
with them in its blessings. 1Co 9:24 Do you not know that in a race
all the runners run, but only one receives the prize? So run that you
may obtain it. 1Co 9:25 Every athlete exercises self-control in all
things. They do it to receive a perishable wreath, but we an
imperishable. 1Co 9:26 So I do not run aimlessly; I do not box as
one beating the air. 1Co 9:27 But I discipline my body and keep it
under control, lest after preaching to others I myself should be
disqualified.
Php 3:8 Yea doubtless, and I count all things but loss for the
excellency of the knowledge of Christ Jesus my Lord: for whom I have
suffered the loss of all things, and do count them but dung, that I
may win Christ, Php 3:9 And be found in him, not having mine own
righteousness, which is of the law, but that which is through the
faith of Christ, the righteousness which is of God by faith: Php 3:10
That I may know him, and the power of his resurrection, and the
fellowship of his sufferings, being made conformable unto his death;
Php 3:11 If by any means I might attain unto the resurrection of
the dead. Php 3:12 Not as though I had already attained, either
were already perfect: but I follow after, if that I may apprehend that
for which also I am apprehended of Christ Jesus. Php 3:13
Brethren, I count not myself to have apprehended: but this one
thing I do, forgetting those things which are behind, and reaching
forth unto those things which are before, Php 3:14 I press toward
the mark for the prize of the high calling of God in Christ Jesus.
Php 3:15 Let us therefore, as many as be perfect, be thus minded:
and if in any thing ye be otherwise minded, God shall reveal even this
unto you.
In light of the context and the versatility of γεγονεναι I would recommend translating like this:
2Ti 2:18 οιτινες περι την αληθειαν ηστοχησαν λεγοντες την αναστασιν ηδη γεγονεναι και ανατρεπουσιν την τινων πιστιν
"...who have avoided the truth by saying that resurrection has already been obtained, subverting some other people's faith as well..."