Nasus's cane strike

As i was trying to see a way to speed up Nasus q stack by maxing out the cooldown and come up with a idea that does not seem to work but it should for example when the champ is equip with hydra blade and/or ice born gauntlet to give Nasus the area of effect of his q hitting then i notice that even if i kill that one lonely minion then attempt to try out the hydra while the q is in active mode ( not striking the minion but still killing them with the a.o.e. of the item) the q did not add up. even more concerning when the iceborn guantlet do the same thing killing other minion within a.o.e. effect i do not get additional stack. i.e. killing 3 minion with q strike does not give me +3 stack of 3 bonus dmg. to the stack.

Active: Nasus empowers his next basic attack within the next 10 seconds to deal bonus physical damage.

Bonus Damage: 30 / 50 / 70 / 90 / 110 (+total stacks of Siphoning Strike)

If the** ability deals a killing blow**, Nasus gains 3 stacks of Siphoning Strike (doubled for killing champions, large minions and large monsters).

Edited for new information:

for Item references so you can see the issue

Ravenous Hydra (Melee Only) Cost: 3300 (600) +75 Attack Damage +100% Base Health Regen +12% Life Steal

Passive: Life Steal applies to damage dealt by this item. UNIQUE Passive - Cleave: Basic attacks deal 20% to 60% of total Attack Damage as bonus physical damage to enemies near the target on hit (enemies closest to the target take the most damage). UNIQUE Active - Crescent: Deals 60% to 100% of total Attack Damage as physical damage to nearby enemy units (closest enemies take the most damage) (10 second cooldown).

(Unique Passives with the same name don't stack.)

Iceborn Gauntlet Cost: 2900 (750) +60 Armor +30 Ability Power +10% Cooldown Reduction +500 Mana

UNIQUE Passive - Spellblade: After using an ability, the next basic attack (on hit) deals bonus physical damage equal to 125% of base Attack Damage to enemies near the target, and creates a field around the target for 2 seconds that slows enemy Movement Speed by 30% (1.5 second cooldown, half-sized field if ranged).

(Unique Passives with the same name don't stack.)