I am a bit confused. My understanding has always been that if an individual were visiting us, and they obeyed the gospel while here, I would direct them to a sound church in their area. They would not be a member of the local church here, although they obeyed the gospel here. If I taught a person the truth, I baptized him, and he lives and works in the local area, would he not be considered a member of the local congregation where I worship?
A person who is baptized is added to the Lord's church. "So then, those who had received his word were baptized; and that day there were added about three thousand souls. ... And the Lord was adding to their number day by day those who were being saved" (Acts 2:41,47). Every person baptized is added to the church in the universal sense. Thus, though the Ethiopian eunuch was baptized while traveling (Acts 8), he became a part of the Lord's church. However, he would have to join a local church or start a local church when he returned to Ethiopia.
We also know that people can move their membership to another local church when they are in a different area. "When he came to Jerusalem, he was trying to associate with the disciples; but they were all afraid of him, not believing that he was a disciple" (Acts 9:29).
We typically assume that a local person who is baptized will be joining the local church. It is the way it ought to happen, but every once in a while I run into people who think they can become a Christian without being a part of any church. Such membership is required by God (see: Can I be a Christian and not go to church?). But since there will always be some who do not obey God, we make it a practice of asking recently baptized Christians if they would like to be considered members of the congregation, just as we ask people who have recently started attending the worship services.