Hi Madison, there is no ‘right’ or ‘wrong’ in your case, as far as leaving them separate or not. Even if they were always kept separate, eventually they’d be calling to each other. Budgies are noisy little things! When they’re happy and healthy, they are a very vocal species!
What I have always done to keep birds quieter in the morning, is to cover the cage at night. Keep a nightlight in the room so it is not pitch dark at night. They ideally need to be in a room that doesn’t get real bright with the morning sunlight. Like a room with a darker curtain or shade. I have found this to be very effective with a lot of birds over the years. That way you can control their sleep/wake schedule.
One bird I have is naturally more of an “early bird” than my others. This bird was previously adjusted to my mother’s very early morning schedule for years. When I took him to my house to live; initially, he would wake up at that time regardless. After some time, using the night cover and darkened room consistently, he finally adjusted to my schedule.
I hope that helps..