From all the Robins, Dick is undoubtedly the one who best accepted his successor (and overall being replaced as Robin) although he's the one who actually created Robin.
Jason and Tim at least knew it became a mantle and could assume that one day they would be replaced.
But overall it seems that some insecurity or jealousy was definitely there at the beginning of their relationship so far (Dick's towards Jason as he was adopted, Jason who felt he couldn't measure up).