The sentence in question: 当時の記録には、役所から住民に対し「隕石を拾った者は届け出るように」と申しつけられていたことが記されています。
My attempt at translation: "Concerning the records from back then, it is written down that it was instructed by the government office to the citizens that 'The person who picks up the meteorite must(?) report'"."
Without an imperative in this quote, it doesnt make much sense that the quotation is called an instruction/order. However, ように as a marker for an imperative is something I havent encountered so far.