Allow me to quote the relevant section, straight from the top-right-hand paragraph on p172 of the DMG3.5E:
Use ECL instead of character level when referring to Table 3-2: Experience and Level-Dependent Benefits in the Player's Handbook to determine how many experience points a monster character needs to reach its next level. Also use ECL with Table 5-1: Character Wealth by Level to determine starting wealth for a monster character
In other words: you only get to count LA for 2 purposes: to determine how much xp you need to reach the next level, and (as a DM tool) to determine how much wealth you should have to be considered "appropriately equiped for your level". Further reading on that page proves what Savage Species started: only hit dice (racial or character) count when determining the number of character feats, attribute increases, skill point maximums, etc.
Or, to put it simply, whenever you read "character level" when playing a character with an LA of +1 or higher, read "hit dice", except in the case of required xp totals, and recommended wealth. Kinda simple, really. The 3.5E FAQ goes as far as stating that the "character level" IS the sum of class levels and racial hit dice, removing all doubt in this regard.
In case of the stated example, this means that said aasimar has 3 level-derived feats (1st hd, 3rd hd, 6th hd), 2 attribute increases (4th hd, 8th hd), and has a skill rank ceiling of 11 (8hd + 3) for class skills and 5 ((8hd + 3) / 2, rounded down) for cross-class skills. Said aasimar needs to have at least 36000xp to have 8 class levels (as a 9th level character), and should have equipment to the value of 36000gp (as a 9th level character).
For that matter, when said aasimar (safely presuming that s/he is good-aligned) gets caught in the area of a
Blasphemy spell cast by an 18th level caster, s/he is immediately killed, without a save (whereas her or his potential 9th level human companion will "only" be dazed for 1 round, suffer a 2d6 strength penalty for 2d4 rounds, and be paralysed and helpless for 1d10 minutes). Think about this (and other "level"-dependent effects), next time you're looking at high-LA templates and creatures.