@Crimsonorblue22 No, sorry about the confusion. I was discussing citizen's arrest generally just as an example where a private person detaining another person is lawful because they are catching a criminal, not in the context of the hazing here where the victim/s apparently were kept from escaping by their assailants. In a case like this unlawful imprisonment may be very means-specific like Dan said (taping someone down), but usually is charged where someone is forcibly kept in a locked room or house.
Just to bring up more of the crap we used to deal with in criminal law, kidnapping involves taking someone unlawfully, whereas unlawful imprisonment involves restraining somebody from leaving, but they are often both charged because there isn't a bright line separating the two.
It isn't just being tied up or handcuffed. It is triggered by forcibly not allowing someone to leave. I have heard of kids filing complaints about being unlawfully imprisoned, but courts give great leeway to parents confining their children within reason. E.g., you can't lock a kid in a room with no way to safely get out in case of fire or accident, and you cannot leave them in a locked room while you go away. You can restrict them (grounding).