Acts refers to 'God fearing' people who heard the gospel. They were already in an old covenant style relationship with God and were now being exposed to the gospel of Christ. Not to go too far off course here, but these are people with the 'water' part of 'water AND Spirit' Christ talks about in John 3:5. They lacked the 'Spirit' part.Acts 16:14, The fact that Lydia was already worshiping God, indicates that she was already born again
God speaks to unconverted people through the enlightening testimony of the Holy Spirit: 1 John 5:9-10. Some choose to retain that testimony and are saved, while others reject it and are lost.Only God's sheep hear his voice.
In general, only kings and priests and other special, called people (i.e. Exodus 34:30-34) received the indwelling of the Holy Spirit in the old covenant. That's the beauty of the New Covenant. Now ALL the people of God have access to the indwelling Holy Spirit are 'in the ministry', so to speak.The old testament saints received the indwelling of the Holy Spirit, the same way that we do in the regeneration process of the new birth.
Moses replied, "Are you jealous for my sake? I wish that all the LORD's people were prophets and that the LORD would put his Spirit on them!" - Numbers 11:29
Moses' was a prophet. His insightful 'wish' was granted in this New Covenant. Now ALL the Lord's people have access to the Spirit that used to be reserved for a special few in offices of ministry in the old covenant. Now we're all in the ministry to one extent or another and have access to this anointing.