Agreed. I thought Tim was very human and sympathetic, as well as very intelligent - all the more impressive since he was "dead" during the storyline.
He's not, at all! He's depicted as angry at Damian, and given the timeline of the issue, that's totally accurate as to his feelings. But he's also portrayed as 1) being Bruce's much mourned son, 2) very loyal to Batman, 3) a detective with strong enough instincts not to send the video to Damian when he made it - Damian only got it because of Tim's death.
There is a hard edge to Tim here - but that's Priest's writing style. Everyone has a very hard edge, even the purest and kindest of characters, like Tanya Spears.
Tim wasn't primarily depicted as jealous of Damian here. He was hurt and angry (which is, again, accurate to what we see in Morrison's run), but also thoughtful, with a secret nerdy side (the name under which he hid the evidence).
I think he was also in the third issue, and Damian mentions him in the fourth (#33).