‘And when they did not find them, they dragged Jason and certain brethren before the rulers of the city, crying, “These who have turned the world upside down are come here also, whom Jason has received: and these all act contrary to the decrees of Caesar, saying that there is another king, one Jesus.” '
Not finding Paul and Silas they turned on Jason and some fellow-believers and hauled them before the politarchs (a term for city rulers local to Macedonia) declaring that Jason had received into his house treacherous people who were know to have caused trouble elsewhere, (they have ‘upset/thoroughly annoyed the world'), and who broke Caesar's decrees, declaring that there was another King, even Jesus.
The charge was a serious one. There were no police, and the legal method in those days was to act on the basis of accusations brought. Thus this followed accepted legal practise in a way that had to be responded to.
‘Politarchs' was the correct term for the city rulers in that area, as we know from inscriptions (in 1st century AD there appear to have been five such politarchs), and they, recognising that correct procedures were being followed, would feel impelled to investigate. Suggestions that Caesar was in some way being slighted were always a guaranteed way of obtaining legal attention. The charge in this case was of treason, of aiming to set up a rival to Caesar. It was similar to the charge that had actually been brought against Jesus.
Teaching about the Messiah, the son of David, and about the Kingly Rule of God, was always open to such misinterpretation and to being twisted by unscrupulous people, as in this case. But then on examination, as in the case of Jesus (John 18:36-37), it would be seen to be what it was, preaching concerning the other world. It was what happened meanwhile, and the effects on the peace of a city, that were the main problems that affected the ministry.