The Roman soldiers ran down to Paul who was being attacked in the Temple.
The Roman were in their fort which overlooked the temple.
Their was a causeway- stairways that joined the 2 places, the Roman Fort, and the Temple area.
A careful reading shows this. So the wailing wall was part of the Roman Fort from which they ran down to rescue Paul.
The temple also had the spring Gihon for washing away the blood of the sacrifices done in the Temple, and they have rediscovered that spring, and it is below the wailing wall in the city of David, where the Temple was located. On what was thought to be the temple mount there is no spring.
Acts 21
Arrested in the Temple
26 Then Paul took the men, and the next day, having been purified with them, entered the temple to announce the expiration of the days of purification, at which time an offering should be made for each one of them.
27 Now when the seven days were almost ended, the Jews from Asia, seeing him in the temple, stirred up the whole crowd and laid hands on him, 28 crying out, “Men of Israel, help! This is the man who teaches all men everywhere against the people, the law, and this place; and furthermore he also brought Greeks into the temple and has defiled this holy place.” 29 (For they had previously seen Trophimus the Ephesian with him in the city, whom they supposed that Paul had brought into the temple.)
30 And all the city was disturbed; and the people ran together, seized Paul, and dragged him out of the temple; and immediately the doors were shut. 31 Now as they were seeking to kill him, news came to the commander of the garrison that all Jerusalem was in an uproar. 32 He immediately took soldiers and centurions, and ran down to them. And when they saw the commander and the soldiers, they stopped beating Paul. 33 Then the commander came near and took him, and commanded him to be bound with two chains; and he asked who he was and what he had done. 34 And some among the multitude cried one thing and some another.
So when he could not ascertain the truth because of the tumult, he commanded him to be taken into the barracks. 35 When he reached the stairs, he had to be carried by the soldiers because of the violence of the mob. 36 For the multitude of the people followed after, crying out, “Away with him!”
Addressing the Jerusalem Mob
37 Then as Paul was about to be led into the barracks, he said to the commander, “May I speak to you?”
