My conure has a real jealous streek in her. We have a tiel & another parrot & a cat. She hates them all! Because she was the last to arrive in our family we've had to bring her down a peg or 2 when it came to the jealousy. It worked, she still hates our other pets but she has learnt to tolerate them & accept they're all here to stay & she is NOT the only one in the house who gets attention.
I think all conures have that jealous streek but you can get ones that are very laid back about other pets. It can also depend on their upbringing. My conures jealousy I believe comes from being in 2 previous broken homes where she lacked attention.
All birds are different & react differently to these sort of things.