No, it's nothing like "work on" or "deal with" (they are phrasal verbs). The structure you're interested in is "get + past participle + (preposition)" and it's very, very common. He got stuck in traffic.
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clin06But how to figure out 'get put inThe author means that he and his associates are placed into an uncomfortable situation, probably by someone in authority or just by the circumstances. In any case he is expressing his displeasure that it happens.