When the clock does strike twelve there is going to be a wee bit of a difference than the seamless transition Momonga got.  For all the characters that transition to the new world, it will be barely a blip on their radar but, the ramifications will be our characters transition into the world a bit later due to slight 'lag' and the major time differential between the two worlds.  For us, it won't be much but it will mean we start our new adventure a bit later than Momonga and crew, putting us coming into the new world roughly at the end of the anime.