Welcome to the community! It sounds like you have a very good relationship with your bird, and a strong bond with him, but it sounds like somewhere along the way you have reinforced his unwanted-behaviors when you're not paying direct-attention to him. You probably didn't knowingly do this, but somewhere along the way he's learned that constantly screaming for you to come back or to pay direct-attention to him works, and it either gets you to come back, or it gets you to talk to him while you're out of the room. So you need to start to put him in his cage whenever you don't want to take him into the room with you, just as you do when you leave the house, and then reinforce that his cage is a good place to be and the place he always goes when you are not with him by using a special "training treat" whenever you put him inside of it.
Something that often helps is actually telling your bird where you are going/what you are doing, and how long you'll be gone. You mentioned "disciplining" your bird, but that is totally the wrong attitude to have and approach to take, because punishment/discipline (Negative-Reinforcement) does not usually EVER work with parrots, they do not work like dogs and cats do. They use logic and reason, and if you try to discipline/punish them it usually backfires and makes the issue worse. Instead, you want to use Positive-Reinforcement (training treat) to get him to do the behavior you desire...Also very, very important is that you never want to use his cage as "punishment" or "discipline", as his cage is his territory in your home, it's his "safe-space" and he needs to always think of it that way and not as a place he's put when he does something wrong, but the place he goes when you aren't with him. So just like you put him in his cage when you leave the house, whenever you want to leave the room that he's in and you don't want him to follow, you simply have him step-up, tell him what you are doing, where you are going, and put him inside of his cage, GIVE HIM A TRAINING TREAT, and shut the door That way he knows that he's not being "punished", but rather it's just time for him to go in his cage and entertain himself for a while)...Then you specifically tell him how long you are going to be gone, and you leave the room. And you don't EVER come back into the room he's in while he's screaming for you.
It's okay to have a "Contact Call" that you use from another room to let him know where you're at and that you're okay, but not screaming...For example, if he's out of his cage and you're in the room with him, and you want to go into another room and get on the computer for a while, you have him step-up, you tell him "I'm going to go and get on the computer for a little while in the other room, so it's "cage-time" or "play-time", and then you put him inside of his cage. Then you give him a special training-treat, shut the door, and then say "I'll be back in one hour", and you then walk out of the room. They very quickly understand how long an hour is, or how long you're usually gone if you're "getting on the computer", and this brings them a sense of comfort after the figure it out, because they know what you're doing and how long you're going to be gone, instead of just thinking that you're leaving them and they don't know when you're coming back, or if you're coming back...After they figure out that being put in their cage is not a bad thing, and they figure out about how long you'll be gone, and they get that treat and know that they're being a good bird, then they will feel more and more secure and comforted, and as long as you have plenty of different toys and things for him to do inside his cage, he'll gradually start to entertain himself happily while you're somewhere else and out of sight.
This is also the same way to deal with the screaming when he can't see you. You do the exact same thing, and if he starts screaming for you after you put him in his cage, you simply cannot return to the room he's in until he stops screaming. Period. And actually being proactive about this and rewarding him by coming back into the room and with a training-treat when he does stop screaming will gradually teach him that "Hey, he comes back and I get a treat when I stop screaming"...But the minute you either come back into the room or start talking to him, or acknowledging him in any way at all while he's screaming for you, then you're inadvertently reinforcing the screaming. So it's all about using positive-reinforcement to get him to do what you want him to do, and never accidentally reinforcing the behavior you don't want.
As far as the "training-treat", it needs to be something special that he loves but that he only gets as a "training-treat" and never any other time. It might be a nut in the shell, like an Almond, or it might be a small piece of some kind of people-food that he likes. Either way you need to make it special for him to get.
That's basically it. You have to train yourself to just handle the screaming for the first week or two of training him this way and using "his territory" to be the place he goes and entertains himself whenever you're not in the room with him, or whenever you're not at home. Also, telling him where you are going and how long you are gone ANYTIME HE IS PUT INSIDE OF HIS CAGE, including whenever you leave the house, will further reinforce using his territory to achieve a wanted behavior and to eliminate any unwanted behavior. So in the morning you say "I'm going to work now, I'll be back later on this afternoon", then give him his training-treat and leave. And he'll soon know that when you go to work you won't be back until later in the afternoon, and he'll have a very good sense of when that is. So he'll learn to entertain himself for that amount of time...And whenever you get home you open up his cage, tell him he's a good boy, give him a training-treat, and then spend time with him...It's all about being very consistent with using his cage and telling him where you're going and when you'll be back, and reinforcing wanted behavior with the special training-treat.
