Baboon, "Put someone on specific time" doesn't mean anything. I will use brackets to try to explain this sentence better: Don't think of the sentence this way: I < put us on the five o'clock > shift for that. Instead, think of it this way: I put us on <the five o'clock shift> for that. "Five o'clock" is modifying "shift." "Shift" means a part of the work day. For example, there could be a morning shift, a night shift, a late shift. If I work the morning shift, maybe I get to work at 7am and leave at 3pm. The "five o'clock shift" is a shift that begins at 5:00. To be "put on the five o'clock shift," means "to be assigned to the five o'clock shift." Was this explanation ok?

It means that you you register or record someone (probably on some sort of time table) who is going to work on a particular shift (e.g. morning shifts/ late shift/ early shift/ night shift/