How many days has this new separation stage been ongoing? one or two?
I would say a week separated is typical.. in that time the newcomer can be given a chance to learn the rest of the rooms in your home (with resident locked away for a bit) and their bedding can be swapped daily (a week is good for scent swapping)...
Has new guy had chance to explore the home yet? ... this is important for him as well as knowing his route back to his safe room.
More importantly at this stage, how bonded is the new guy with his humans now?
Can you pick him up at will? .. can you handle him and touch him all over without fear or protest?
I suggest your next stage could be to introduce yummy food (fish is good) for both cats to eat either side of the saferoom door.... this will get both cats close together while experiencing a positive yummy mealtime.. they will transfer that positive association to ''being together = good things'' ... thats the idea anyway but repetition and consistency are key.
After these shared mealtimes (behind the closed door but next to it) become normal for them with no hissing or fuss (few days all being well) you could then try real shared mealtimes... separate the bowls from the door location to the far end of the two rooms the cats are in (new guy's safe room and resident in adjoining room) and serve them a meal at same time again - but open the door during the meal.... try to do this in a relaxed manner with no drama and keep yourself between them and in a spot where you can close the door if either of them stop eating and head towards the other.
Close the door after the meal and congratulate yourself EVERY time you create a session like this
that ends positively.
Once kittys are happy to eat an entire meal in sight (and scent) of each other without any fuss or fear you can build on these sessions by allowing them to interact for short periods after their mealtime... and GRADUALLY extend the length of they spend together in these post-meal sessions.
Its really important that every meeting you create ends positivity with them not having any fear or anger to each other.. if they are still keen to be together when the timer goes to separate them thats a good thing too (but still stick to the plan and separate them - extend their next session as appropriate).
Lets see if you can get suggestions here on what exactly to do with them when they are together during these early meetings...
I think having a helper with you and engaging both in separate play (with wands or toys) in the same room is a good start.. distraction is a powerful tool for you... if you just sit back and let them do what they like with no interaction from you they will go right back to rough housing and resident may start to dominate/bully and upset the new guy again.
Be patient and dont rush anything.. remember they have the rest of their lives together now ... and these early days of introduction really do ''set the tone'' for how well they get along in the future.
If it takes a month or two its well worth it if they form a close bond of friendship for their lives together.
Have you shared any pics yet?