Does controlling a figure with the Soporific Musk card make it the Slanneshi player's figure for that turn? Or does they control it, but ownership remains with the original owner?

I had control of an opponent's cultist using that card, & some affect said something like "kill an enemy's figure". Could the opponent have killed his own cultist that was controlling for that turn?

It is Slaanesh's figure 100% for that turn. So Slaanesh can't target it in battle and the original owning player can treat it as an enemy.

Slightly off-topis but "soporific" was Dictionary.com's word of the day today.

and what about upgraded khorne cultists? does they lose theirs 1attack when slaanesh takes control of them? its khorne unit after all but under slani control...

Vitalis said:

No, you take control of the cultist. The cultist remains what it is in all other respects - so doesn't gain a toughness if Slaanesh has the cultist upgrade and retains the 1 attack if it was an upgraded Khorne cultist

Another question. When does the controlled figure attack? Example scenario from last night's game: Slaanesh takes control of an upgraded Bloodletter that can take out figs before they can strike back. Tzeentch also has a Horror in the region. Can Slaanesh use the Bloodletter to take out Tzeentch's Horror before it can attack Slaanesh's figures? Or does Slaanesh have to wait until after Tzeentch goes to have the controlled Bloodletter attack along with any of his other figures?

I argued that Slaanesh acts after Tzeentch due to dial order regardless of whether the figures he is using are his own or those of another player that he temporarily controls. Others argued that the Bloodletter was still a demon of Khorne, regardless of being controlled by Slaanesh and so went before Tzeentch.

mac40k said:

The controlled figure has the abilities it had before it was taken. The Bloodletter strikes at the start of the combat round regardless, then we revert to normal attack order. So yes, the controlled bloodletter could kill the horror before it could strike back, and at the same time as any other Bloodletters in the region

Also - I assume it was taken control of by the upgraded Keeper of Secrets, yes? Because Soporific Musk specifically states it takes control of a CULTIST

What about Corruption Tokens during the Corruption phase?
If e.g. the Slaaneshi player controls a Khorne cultist via Soporific Musk or Changer of Ways upgrade, who gets to place a Corruption Counter in the region? Controlling effects clearly state that figures are controlled until the end of the round...

If the above-mentioned Slaaneshi-controlled Khorne cultist would survive until Corruption Phase, he would per definitionem be the Slaaneshi-players cultist, right?
That means that he can place one more Corruption Counter...
Or is he not allowed to do so, but the Khorne-player cannot place a Corruption Counter for him?
Or can the Khorne-player still place a corruption counter since the figure is, in any way, still a Khorne cultist, although not "Khorne's cultist" at the precise moment...

If Slaanesh controls the Khorne cultist, Slaanesh is putting down the corruption token.

Note that it only lasts as long as the end phase, so by the time you resolve hero tokens it's not yours anymore. Otherwise it's 100% yours. You can even summon it elsewhere if you like