Hey Sopho,
There are a couple things that you have to know before coming to any conclusions. The quote that you’ve cited (the one attributed to St. Polycarp himself) is actually taken from the Martyrdom of Polycarp, a work which takes the form of a letter from Smyrna to other second century churches of Asia Minor. The Martyrdom is usually considered to have been composed during the latter half of the second century AD, but some modern scholars believe it was composed around the early third century. The historicity of the Martyrdom has come under some skepticism based on accounts that parallel those of the passion narratives in the Gospels. While such accounts are possible, it is more likely that the parallels are literary devices, rather than historical events. Therefore, the Martyrdom is written as a treatise independent of St. Polycarp’s actual martyrdom. In fact, the quote you cited may not be authentic to the saint himself.
For more information, see: en.wikipedia.org/wiki/Martyrdom_of_Polycarp#Historicity.
I would suggest reading the epistle of Polycarp to the Philippians for what I believe to be an authentic work of St. Polycarp himself. As far as I have read into the epistle, I can’t see any hints of ECT teachings within it. It is an NT-based exegesis containing instructions for the Christians at Philippi in Greece.
Concerning Theophilus of Antioch, some claim that he was an annihilationist, not an ECT-advocate. The doctrine of conditional immortality teaches the annihilation of wicked, mortal souls in Gehenna. However, depending on what translation you read of his Apologia ad Autolycum, it would seem he speaks of “eternal torments” in the “hereafter” (Book I, chapter XIV). Now, it is obvious to me that Theophilus deliberately misapplies and/or misinterprets St. Paul’s words in Romans 2:7,8. Theophilus claims that the suffering of the wicked will endure for eternity in the afterlife, while Paul says nothing of the sort. Rather, Paul is referring to the day of judgement for Jews first, then for the Greeks (Romans 2:9,10).
In any case, I wouldn’t look upon Theophilus of Antioch as an inspired source, though he was a skilled apologist. What I don’t understand is how, and from where, you learned that St. Polycarp was associated with Theophilus? I can find no direct or close connection between the two.