Matthew 12:28

“But if I by the Spirit of God cast out demons, then is the Kingly Rule of God come upon you.”

So having demonstrated that He (emphatic) cast out demons by the Spirit of God, that has really demonstrated that the Kingly Rule of God has truly come upon them. It could no longer be doubted. And this was because in His case He was doing it as the son of David. It demonstrated quite conclusively that the Kingly Rule of God was therefore now here and present among them. By this Jesus connects the Kingly Rule of God with present activity of the Spirit. This also demonstrates that all who are in the Kingly Rule of God are enjoying the blessing of the Spirit well prior to Pentecost. It also demonstrates the presence of the Kingly Rule of God, not as something temporary, but as something permanent. It is here all the while that the Spirit is at work among men.

Note the use of the rarer (in Matthew) ‘Kingly Rule  of God '. This links it directly with the Spirit ‘of God' and avoids any idea that God is not Himself totally involved in this. It brings out the living God's direct opposition to Satan in Jesus.

The link between the Holy Spirit, and the coming Kingly Rule of God and renewing of the true Israel, was common in the prophets, and described in various ways. See for example Isaiah 32:15; Isaiah 44:1; Ezekiel 36:24; Ezekiel 37:1; Joel 2:28. It was confirmed by John the Baptist (Matthew 3:2 with 11). So Jesus was now giving a mighty visible evidence of the fact that the Kingly Rule of God was present among them.