For (gar). Luke adds the reason for the wild charges made against Paul.
They had before seen (ēsan proeōrakotes). Periphrastic past perfect of prooraō, old verb to see before, whether time or place. Only twice in the N.T., here and Act 2:25 quoted from Psa 16:8. Note the double reduplication in ̇eō̇ as in Attic (Robertson, Grammar, p. 364).
With him in the city Trophimus the Ephesian (Trophimon ton Ephesion en tēi polei sun autōi). The Jews from Asia (Ephesus) knew Trophimus by sight as well as Paul. One day they saw both of them together (sun) in the city. That was a fact. They had just seized Paul in the temple (hieron). That was another fact.
They supposed (enomizon). Imperfect active of nomizō, common to think or suppose. Perfectly harmless word, but they did, as so many people do, put their supposed inference on the same basis with the facts. They did not see Trophimus with Paul now in the temple, nor had they ever seen him there. They simply argued that, if Paul was willing to be seen down street with a Greek Christian, he would not hesitate to bring him (therefore, did bring him, eisēgagen as in Act 21:28) into the temple, that is into the court of Israel and therefore both Paul and Trophimus were entitled to death, especially Paul who had brought him in (if he had) and, besides, they now had Paul. This is the way of the mob-mind in all ages. Many an innocent man has been rushed to his death by the fury of a lynching party.