Yes, nightbot needs to be present in the channel for him to show up as a mod in the tmi.twitch.tv/group/user/drdoomtastic/chatters list. However, he himself is not a mod on the /mod list.
This image shows him receiving mod status, while your image shows that he is in fact, not a moderator.
(You can check this yourself, when MOD: Nightbot shows up on chatty, the api link also shows nightbot as a moderator).
Again, there are no real issues with all this, it’s just a major annoyance to have a properly working system changed into this mess.