It looks to me like he gets the 15 mil bonus in 2010 according to the article. He played in 35 percent of the offensive plays in his rookie year.
Leinart can make $15 million more by simply playing a minimum amount of time in any of his first four seasons (that's either 35 percent of the offensive downs as a rookie or 45 percent in years 2, 3 or 4).
It also appears that had he played more, he would have a 23 mil cap hit in 2010.
The first escalator raises Leinart's base pay by $8.5 million in 2010 if he either plays 55 percent of the offensive snaps in two of the first four seasons or 70 percent in any one season (the Cardinals must also reach a team qualifier – which states an area of statistical improvement – under those two scenarios, but that's not considered difficult).
I'm not as good as Joe with this cap stuff so its quite possible that i'm incorrect, but thats just the way i'm reading the info from the article you posted.