I have a sun & jenday. I had my jenday for over 10 years before I added my sun. I did let them out together right away. They did bicker, and lunge at each other. This took some time to settle down. I’d say a few months. My sun surprisingly stepped up already (he did this the first day I brought him home). He enjoys sitting on my shoulder. His previous owner must of handled him quite a bit. He just popped out of his cage immediately. He begs to come out first thing in the morning, and continues to do so all day long. Maybe I just got lucky?
If you do choose to let them out (without seeing how your conures are it’s hard to make a suggestion), I’d try to only let one out at a time for a more controlled environment. I use sun flower seeds as a high reward for my conures to bribe them. I feed them pellets so a sunflower seed truly is a delicious treat for my conures. Have treats ready when you let them out especially at first. I do agree with the above poster. When I moved 2 years ago to my new house. My Jenday wouldn’t come out of her cage at my old house so we could get her cage in the moving truck. I had to physically intervene by putting on gloves and removing her from her cage. She didn’t come out of her cage at the new house for days. She was so scared of me. So be very very careful when you let them out. If you truly do have to physically intervene to get them back in their cage. If you don’t already have a bond with them they may not be forgiving.