Adam Clarke on Acts 16:20

Brought them to the magistrates - Στρατηγοις, The commanders of the army, who, very likely, as this city was a Roman colony, possessed the sovereign authority. The civil magistrates, therefore, having heard the case, as we shall soon find, in which it was pretended that the safety of the state was involved, would naturally refer the business to the decision of those who had the supreme command.

Exceedingly trouble our city - They are destroying the public peace, and endangering the public safety.