That baptism is for believers is shown in many passages.

On the Day of Pentecost it was those who received the word preached by Peter that were baptised (Acts 2:41). His preaching had included the need to repent (Acts 2:38). In Samaria it was men and women who believed Philip's preaching of the good news about the kingdom of God and the name of Jesus Christ who were being baptised (Acts 8:12). Many of the Corinthians were believing and being baptised (Acts 18:8). And the Gentiles at Cornelius' house had already received the Holy Spirit (Acts 10:47).

Ananias tells Paul to be baptised whilst calling upon the name of Jesus (Acts 22:16). Lydia's heart had been opened by the Lord to respond to the things spoken by Paul (Acts 16:14-15).

An open heart, repentance for sin, responding to, receiving and believing the preached word, and calling upon the name of Jesus. Clear indication that these people were believers.