Hi guys/ladies, I'm actually going to be busy for a few days, but I just wanted to drop by to express my interest. 

Why can't both happen at the same time? Maybe there was an increase of missing witches cases and/or murder of witches for the past few weeks/months/years prior to the Emergence. Despite that, as is their custom, the witch families can have their masked-witch-unity party and initiation for the newcomers. Since most, if not all, the witch families are already there, the leaders (head of each family) can have a conference about the threat of the Hunters. 

They can make a "peace treaty", but whether anyone upholds it can be a different matter. If the feud has been going on long enough, I'm sure someone's going to backstab someone sooner or later. I mean, isn't this the perfect time to get rid of someone and blame it on the Hunters? Even if it wasn't intentional, a little misunderstanding could turn into something nasty very quickly. 

…Or the main leader can get promptly assassinated during the whole party :)