Lunatic Eruption - (when does its first effect start?)

Rémi wrote:

Dear all,

I have not found confirmation about those situations:
- 1 - Madness Network is in play.
I perform a successful Lunatic Eruption on an untapped Malkavian vampire controlled by my prey.
When I give the action impulse to my prey, must they activate the Lunatic Eruption through Madness Network or may they decide not to act?

- 2 - Lunatic Eruption on my own vampire
I perform a successful Lunatic Eruption on an unlocked minion I control. Does the mandatory action granted by Lunatic Eruption go up at end of the actual action or does it have to wait until my next action phase.

- 3 - Madness Network is in play - part 2..
My own Malkavian vampire has a Lunatic Eruption. Can that vampire rush during each player's turn through Madness Network?

- 4 - Enkil Cog
Am I correct to assume that any answers related to Madness Network would be the same for un unlocked Enkil Cog?

Card Text:
Lunatic Eruption:
Put this card on any ready minion. During his or her minion phase, the minion with this card must enter combat with a ready minion controlled by his or her prey as a Ⓓ action (unless the minion must hunt). Any minion may burn this card as an action.

Madness network
Put this card in play. Unlocked Malkavians can take actions in any Methuselah's minion phase (follow normal sequencing rules). Any minion can burn this card as an action that any unlocked Malkavian (in addition to the normally eligible blockers) can attempt to block.

Thanks in advance,
Rémi.

Name: Enkil Cog
[KoT:R, Anthology:1, 25th:1]
Cardtype: Action Modifier
Unique. Requires a vampire with capacity 10 or more. Only usable after resolution of a successful bleed against your prey.
Put this card on this vampire. This vampire gets +1 bleed. During any Methuselah's minion phase, this vampire can lock this card to take an action.
Artist: Marian Churchland; Ginés Quiñonero; Marian Churchland