Apparently, if I use the update_collector_detail method to add new collection terms (and presumably to remove collection terms, too), those changes don't take effect until that collector has been restarted. I can't imagine a use case where someone would want to update collector parameters but not have those updates take effect, so I think it's logical to have the collector automatically restart when update_collector_detail is run.
Also, updates to collection terms won't take effect in how the processor builds track_kw, so it might be good to automatically restart the processor, too.