I think you may be getting all the bonuses, even though it just has each bonus marked as tier 1. I am using Ash Warrior armor, so to check, I took it all off. With no armor, health 558, lt.armor 81, equipped bow damage (basic) 68. The total perks for the 4 set items (given by the armor itself when worn, these 3 that I can check) are health +33, lt. armor +30, and bow damage +10%. So without any set bonuses, I would expect health to be 558 + 33 = 591, lt. armor to be 81 + 30 = 111, and bow damage +10% to be 75.
The 3 set bonuses (the ones I can check) are all shown as tier 1 : +11 health, +9 lt. armor, and + 10% bow damage. If all of these set bonuses are applied I would expect my health to be 591 + 11 = 602 which it is, lt. armor to be 111 + 9 = 120, which it is, and bow damage to be about 75 + 10% = 83, and it is actually 86 -- can't explain that.
So, I am receiving all the set bonuses (the ones I can check) even though it is just showing tier 1 for each set bonus. Maybe you are too and the bonuses are just mislabeled all as tier 1.
edit - Just out of curiosity, I checked the set bonuses for my Tracker armor, and it showed bonuses of tier 1, 2, and 3, but the bonuses of the 3 items I checked above were health +5, lt. armor +7, and bows +7%, which is consistent with the set's slightly lower level, and indicates that the Ash Warrior's 3 tier 1 bonuses are actually the tier 1, 2 & 3 just mislabeled.