Even if you had a hand-tamed adult re-home, you could end up getting similar reactions until you had built trust (most adult birds in a brand new environment aren't just going to trust someone new right away). When you force it by trying to touch him and scaring him, you res-set your trust bank back to 0 each time..Think of trust as a bank..you can deposit, spend all of your money or even go into dept if you over- withdraw. Now, you can make deposits to rebuild your savings, but it takes time, and you have to pay off debt first.
You can still build trust with this bird, but you have to get better at reading your bird and understanding how this all works in terms of building trust. He doesn't know you, he doesn't know your house, he has had a rough time of it and heck, if he was never let out before, he could also be cage-bound (cage-bound birds can become un-cage bound, but you have to start by understanding all of this).
By ignoring his body language, you are likely frightening him. You should never ever try to contact a brand new bird right away unless they show interest..It's a lot different from dogs and cats who adjust much more quickly to new people.
Here are some sort of goofy scenarios to help you understand a bit better how your bird may be feeling....Not saying you are trying to date your bird, but it's the best thing I could come up with...LOL- It's not a perfect analogy....
Scenario 1: You smile at a cute stranger on the street as you are passing them. They run over to you and give you a kiss right on the lips. Your reaction would probably be fear, anger, shock, panic, confusion, nervous laughter? Now imagine of this person was trying to do this each day...At first, they were just unfamiliar because they were a stranger, but after the whole incident, you would be on the look out and cautious of this person. If it happened once, it would be weird and startling/upsetting, but if it kept happening, I imagine you would become super scared and start preparing to defend yourself etc. If you didn't already the first time.
Scenario 2: you smile at a cute stranger on the street. They smile back. You see them the next day at a coffee shop and they strike up conversation about whatever, but you both do your own thing after the brief chat. You bump into them a lot because you work in the same area and you both like coffee blah blah. You join that person for coffee one day and give them your number because you've spoken with them quite a few times and they seem interested. They call you and invite you on a date. You go on a few dates (ALWAYS LOOKING for any red flags on those early dates)..Is he/she a weirdo? Does he/she respect boundaries? Does he/she treat you/ others well? Eventually, you may decide you really like this person etc...
Scenario 2b- alternate ending:
* Now, in scenario 2, you might go on a date with the same nice person from scenario 2, but they tell you they are 41, live in mom's basement, never had a job, and only eat foods that start with the letter z... you might lose some of that trust that you had for that person, right?
Trust is fluid...it can be built or destroyed. Luckily for you, humans in the dating world are not likely to recover from mis-steps, but YOU can re-build trust with your bird, as long as you are patient and realize that you can make things worse if you keep pushing.
Slow way way way down.
I got a tamed but adult cockatoo and couldn't touch her consistently for about 2 months and she wouldn't step up until 3...My bird knew how already, but I was her 4th home...yours may or may not know how to step up and everything is new right now (including you and your 2 other birds)..so a week is like 1 second in bird time.
Also---putting your hand into the cage is not the first place you should start if you do touch your bird, and none should be attempted right off the bat unless the bird is cool with it. That is often their safe-space and a hand reaching in can feel like they are trapped and also that you are invading their space. Eventually, once a bird trusts you, you will likely be able to do this, but that is a ways away.
During bonding, keep yourself as low-stress as possible to the bird. If you standing by the cage upsets the bird, don't get so close right away. Hang out in the same room, maybe 10, 8 or 4 feet away (depends on the bird) but read quietly outloud...or as you do things in the room, talk about what you are doing.
I am not saying walk on egg-shells either-- I mean, you have to be able to pass by the cage etc-- so don't think I mean that you have to tip-toe around, but if your presence is frightening to your bird early on, then try to back off a little to show that you are not a threat.
Let the bird see you put a treat in its bowl, but don't try to feed from your hand if the bird hesitates (again, you have to move at the bird's pace and your goal should be NOT to scare him, even if you think he''s silly for being scared). So, you can feed the bird from your hand if the bird doesn't hesitate, but if it does, that alone could be a source of stress initially.
Questions for you that could help with further trouble-shooting:
1. Can your bird fly?
2. Did it ever spend time out of its cage in the past/was it handled in its past situation?
3.Can you describe the situation it came from?
4a. How old were your other conures when you got them?
4b. How old are they now *current age really does matter*?
4c. Where are they located in comparison to this new bird?
5.Has the bird been checked by an avian vet?
6.How much sleep does he/she get nightly?
7.Are there any shadowy spaces (huts, boxes, tents, tubes, hammocks etc in the cage)?
8. How big is the cage?
9. What does his diet look like on a daily basis?
10. Do you allow him to go back into his cage when he chooses, or have you been toweling him to put him back in?