Good catch.
Acts 13:1-3 - Under the direction of the Holy Spirit Antioch sends out Paul and Barnabus as apostles. Acts 15 takes place after this missionary journey by Paul and again it the congregation of Antioch that sends Paul and Barnabus to deal with a problem stemming from Jerusalem. After the problem is dealt with at Jerusalem Paul and Barnabus return to Antioch. Jerusalem sends two prophets of their local congregation, Judas and Silas to accompany Paul and Barnabus to Antioch. Vs 33 reports that after they had spent some time there, the Antioch congregation sent "them", apparently Judas and Silas, back to their home congregation of Jerusalem. The difficulty is that vs 40 has Paul departing from Antioch with Silas for another missionary journey. The alternate wording of Vs 34 has Silas remaining behind.
If you look at these scriptures Antioch does not really appear as a subordinate church to Jerusalem. Under the direction of the Holy Spirit they had authority to send Paul out as an apostle and later dispatch him to sort out a problem caused by some from the Jerusalem church. Antioch received emissaries Jerusalem, Judas and Silas, and also dispatched at least one of them back.
From the New Testament writings it doesn't appear that Paul returned to Jerusalem again until just before his arrest. This would mean that either Silas elected to stay behind or returned to Antioch some time later. I would go with the first.