From the meaning of the sentence, I am leaning towards your turn of event description although I find it hard to see a difference between the two. There is certainly a direct-contrast type of element in the entire thing but I feel the main importance is on the sequential aspect where the later situation is substantially different from before because of how time passed. In any case, you should view dann aber as belonging together. This is supported by different variants of moving the two into other parts of the sentence:
[…] er wird dann aber in einen regelrechten Kampf verwickelt.
[…] in einen regelrechten Kampf wird er dann aber verwickelt.
[…] er wird aber in einen regelrechten Kampf dann verwickelt.
It feels best to keep the two together.
Aber cannot be a conjunction here, because it is not in zeroth position — the entire first position is filled by dann aber which is also not a conjunction as a whole because it is immediately followed by the finite verb.
The entire dann aber is used adverbially. And to the best of my knowledge I would say that both its fragments are adverbs, too. We can construct the sentence with both halfs of dann aber (but one requires reordering):
[…] dann wird er in einen regelrechten Kampf verwickelt.
[…] er wird aber in einen regelrechten Kampf verwickelt.
And it is also possible to pull dann and aber apart:
[…] dann wird er aber in einen regelrechten Kampf verwickelt.
My feeling tells me that this last version focusses on the aber more, and may come closer to what you called direct contrast.
Having aber in first position would usually turn it into a conjunction, by the way:
[…] aber er wird (dann) in einen regelrechten Kampf verwickelt.
(Note how er now occupies the free first position since aber has zeroth.)