بَادِيًا صَدْرُهُ مِنَ الصَّفِّ means that the man's chest visibly projected from the line. بَادِيًا means “showing or apparent,” صَدْرُهُ “his chest,” and مِنَ الصَّفِّ “from the row.” A visible irregularity prompted renewed instruction.
The incident does not authorize humiliating someone over a minor mistake. When possible, row alignment should be corrected calmly before the takbir, with clear guidance and consideration. Shoving or harming another worshipper is not a proper method of correcting a row.