It has to do with Lin and Asik being restricted free agents with Early Bird rights.
The Bird exception allows teams over the cap to re-sign their own free agents. It takes three seasons for a team to have full Bird rights to a player. The Early Bird exception is similar, but it applies to players who have only had two seasons toward establishing Bird rights. The Early Bird exception only allows teams to re-sign their own free agents up to a salary near the league average (apparently it's 104.5% of the previous season's average salary).
A previous loophole in the CBA was exposed when Gilbert Arenas became a free agent after his second year in the league (he was a second round pick). Golden State, with Arenas' Early Bird rights, could only offer him a starting salary around $5 million per season since their team was already over the cap. Washington, who had a bunch of cap space, were able to offer Arenas a contract that started around $8 million and averaged about $10 million a year. Even though Arenas was a restricted free agent, Golden State couldn't match because it exceeded that $5 million starting salary they could offer with Early Bird rights (and no cap space).
So the Arenas provision was put in place in the 2005 CBA. Restricted free agents with one or two years in the league are now limited to offer sheets that start near that league-average mark (the aforementioned 104.5% of the previous year's average), which allows a team to use the Early Bird exception to match an offer from a team with cap space; last summer, that figure was set at $5 million (due to the lockout messing up the previous season's figures). The second year can only be a 4.5% raise on the first year's salary; last summer, that was $5.225. The third year is where it gets tricky.
Asik had only played two seasons, so the Bulls only had Early Bird rights (and no cap space). The Rockets were able to offer Asik 3 years, $25.1 million because they had more than $8.37 million in cap space (the average salary of that contract). The Arenas provision gave the Bulls a chance to match using their Early Bird rights with a 5/5.2/14.9-structured deal. That third year would have especially problematic due to the new progressively harsh luxury tax. Lin's situation was the same.
I believe Houston is actually paying both Lin and Asik 5/5.2/14.9 each year, but for salary cap purposes the annual hit is 8.37/8.37/8.37. I think that's why
one site shows the former and
another shows the latter.