Do we add implement bonuses on that ? What about ability score bonuses ? (Spells)

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I have some questions.

One of my character is my campaign is a infernal warlock.

He's got hellish rebuke and fiery bolt. He was arguing at last game that he should add his implement bonus on bonus damage rolls of those spells.
I know the spell is IMPLEMENT, but I never thought that those spells were meant to be this way.
Yet... what damage do we NOT add on those additionnal dices ? For example, my warlock is a elf, with valenar weapon training (+2 dmg with falchions and with multiclassing in swordmage he's using the falchion as his implement) and it seems wrong to me to let the +2 on the splash damage of fiery bolt.


To compare, the sorcerer really adds his strength/dexterity mod on his damage rolls. For example, I can assume the sorcerer would do 1d6+str/dex mod on the AoE damage of Explosive Pyre and I'm totally okay with that but I can't think that he would add on top of that his implement bonus.


Thanks in advance for answering me !
If a power has the implement keyword, then you add the enhancement bonus of a magical implement to its attack roll.  If the power also has a damage roll (as opposed to dealing zero, or a set amount of damage), then you also add the implement's enhancement bonus to the damage roll.

For example, the user of Fiery Bolt will add his implement's enhancement bonus to its attack roll, and its damage roll (the 3d6+Con Modifier), but not to the Infernal Pact kicker, which does not have a damage roll (it deals a set amount of damage).
Another day, another three or four entries to my Ignore List.
Thank you very much.
Yay things that are explicitly stated in the PHB!
"Invokers are probably better round after round but Wizard dailies are devastating. Actually, devastating is too light a word. Wizard daily powers are soul crushing, encounter ending, havoc causing pieces of awesome." -AirPower25 Sear the Flesh, Purify the Soul; Harden the Heart, and Improve the Mind; Born of Blood, but Forged by Fire; The MECH warrior reaches perfection.
Still, thank you