Separate the outputs for each sample in Abbey road drums to route it inside ableton

Hello everyone,
I just bought the Abbey road drummer bundle, so I'm pretty new to kontakt, and I gotta admit I'm pretty lost with its interface.

My problem is : I want to route each part of the drum (snare, kick, hihat...) Inside Ableton's drum rack, or external tracks so I can mix properly each sample. I watched videos about it, and now I can route each channel of the Abbey road's mixer into separate tracks with the output menu of kontakt (yes ! I guess this is a first step ahah).
But I still have a huge problem which seem to be relative to the way Abbey road drums sends the sounds into its own mixer : each channel of the mixer receives the signal of others samples. For example, when I hit the kick, it goes through its own channel (the kick one, which is normal), but it also goes through the snare one, and the Toms ones. And this is the same for the others samples. So the snare channel, for example, is always receiving signals from the others sample (the intensity of these externals signals is low, but it still exists and make the snare pretty hard to compress since it contains other sounds into it, like Toms, cymbals and mostly, kick). I tried to mute the overhead channel, but the problem is still there. It seem to be relative to the way Abbey road drum is routing the sample signals into its mixer, mixing every signal like if the mics recording the snare was also getting a little part of the sound of the kick, and the Toms (like in some real drum record).

So my question is : is it possible to isolate the signal of each sample (or part of the drum) to its correspondant part of the mixer ? Is it possible to make that, in the snare part of the mixer, I only got the signal of the snare, and the same for the Toms, the kick etc... ?

Thanks a lot for reading me, I'm sorry of this question was already asked (didn't found it in the forum for the moment), please let me know if it is.