To my understanding in conventional wisdom (and standard DM D&D rules) "you hit", refers to you yourself or your primary spell hits, not your splash aka blast damage, it has to specify splash aka blast damage and what the implement your using says..
See above for things the books don't say or even hint at. Splash damage is not a game term in D&D4th edition, even tho there are powers that approximate the concept.
Acid Arrow!
The Sorc power Prime The Fire:
Crap!
2d8 + Charisma, Area burst 1 within 10 squares.
You forget the target: line, which is mentioned above. All enemies in burst.
Every enemy in that burst is a primary target.
You hit a primary target within ten squares, but it bursts out and hits everything with splash (*aka BURST*) damage, within one square.
No rule in existance requires that the point of origin for any area burst be a creature. Please refer to pages 271 and 272 for instructions on how to resolve powers with the Area attack-type, and with range burst x in y.
IF it says "whenever you hit an enemy", the first initial enemy targeted, not those affected by the burst damage are the ones that are affected by the "whenever you hit an enemy" modifier.
Except the power does not work this way, so this interpretation is meaningless.
Did you roll attack dice against them? Yes. Did you succeed against their defense? Yes. You hit them. Enjoy your hit-triggered effects on said target.
But as Prime The Fire says you have to use an implement with it.
Minor correction. The Implement keyword does not require you have an implement to use that power. It says you -may- use an implement you are proficient in, and apply its enhancement bonus to attack and damage rolls.
If the implement says it has a 'when you hit with' it modifier, than it's safe to assume that yes, it does count even for your splash/burst damage however, if it does not, it is the target you hit as your primary target and none others.
If the implement says that it has a 'when you hit with it' ability, then you can use it whenever you hit with a power. It does not matter if it's the first, second, third, fourth, or fiftieth target you hit this round. It does not matter if it's in the center, one square to the side, or at the very edge of the burst. The ONLY thing that matters is: Did you hit it? If yes, process ability, if no, do not process ability.
Does that make any sense?
No, because this idea that you're putting forth doesn't actually match what the power does. The power does something completely different than what you describe. What it does is it selects an area (a creature does not need to be in the center of that area) and it attacks every creature in that area. With fire. And hit or miss, every creature targeted by it takes damage if it attacks before your next turn. And because it is an implement power, every damage roll in that power adds your enhancement bonus. And any creature you hit applies any 'when you hit' effects. And any creature you miss does not have those effects applied.
What YOU are describing is something like Acidic Implantaiton (PHB2, Sorcerer Attack 5) which IS an attack against a single primary target, that follows up with secondary attacks against secondary targets.
Guess what? You're still attacking those secondary targets. Guess what? You're still hitting or missing them. Guess what? Those hits totally count for effects that trigger on hits. Why? Cause you hit. Those effects don't CARE if it's the first, second, or ninth creature you've attacked... they just care if you hit.
That said, there are times where 'splash damage' does not involve hitting or missing. Those won't involve attack rolls... it'll just say 'and do damage to all adjacent creatures' or it will say 'Effect: Deal blah damage to adjacent blah' or whatever. They won't involve making attack rolls against them, so you can't hit nor miss them. You only damage.
I think I get where the confusion lies... if you have a hit line, it will often say 'Hit: The target takes so and so damage' even for multitargetting powers. This is for consistancy. You process the Hit line for -each individual target hit-. As an example:
Cylcone of Restoration Spinny Healer Dude Attack 20
Daily - Divine, Healing, Weapon
Standard Action - Close burst 1
Target: Each enemy in burst
Attack: Strength vs. AC.
Hit: 2[W] + Strength modifer damage, and an ally within five squares of the target may spend a healing surge.
Effect: The target grants combat advantage. All allies within six squares of you gain temporary hit points equal to your Wisdom modifier.
If you hit three enemies with this power, that means that each enemy is hit, each triggering your hit-related triggers, and more-over, each enemy hit also causes an ally to spend a healing surge. 3 hits, 3 healing surges. This is because you process the hit line once per each enemy you hit. Then, yes, the effect says 'The target' but it is always assumed that 'The target' can refer to multiples or singular targets, so long as the target line of the power is satisfied.
Note that "primary target" is not referenced at all in the rules for area attacks, nor does it exist as an entry in the Compendium.
Primary Target does still exist in the game, however. But... it's related more to powers that have multiple attack 'phases' like Force Orb, that has a secondary attack. But, if you have an ability with a Primary attack, then you're pretty much guaranteed a secondary attack.