My cockatoos have always been indifferent to the other species of birds...until Buddy the Nanday came to our house. Milton and Buddy have similar personalities, and took a rather immediate dislike towards each other. I believe that Milty's pulling of feathers was partially caused by seeing us interact with Buddy...and whenever their cages are in the same room, they argue and yell at each other.
Buddy is indifferent (to use the same word again) with his dealings with our tiels and budgies. They all live in the same room- in separate cages. When they are out of their cages- which is most of the daytime- they keep to themselves. The tiels like to go into Buddy's cage to steal his food, and that naturally gets Buddy upset. He'll chase the thief out of his cage and then guard his food.
Milton has his cage in our bedroom, away from the littles. I believe that is the best setup for us...I do not trust Milty's big beak with the littes...at all.
Tiels are calm, laid-back souls...and other species seem to pick up on this, and will sometimes pick on them because of that fact. These are just my observations based on the birds I've "owned", now and in the past.
That all being said, there are many people who have small and larger sized species together in an aviary-type setting, with success. I believe that a key to this success is that the birds can FLY, thus being able to get to safety when needed. Another key is that the aviary is large enough so the birds can have very definite "favored" spaces for themselves.
One other thing...if you do bring a conure of any species into an area with tiels, make sure you set up an air purifier to cut the tiel dust down for the conure...we have three machines running because of Milton, Igor, Mocha, and Sunshine...and I'm considering a fourth machine...