I am a Logic user, and I'm pretty sure I understand what you're saying.
So, with the exs24 you have ADSR settings on the front GUI in bottom right,
as well as "playback" settings internally within the exs24.
My guess is that the "1shot" box is checked, and your current ADSR settings do not cut the samples off.
In the biggest screen shot at the bottom, you can see that I have an 808 kick that I am editing in the EXS24 editor. I have "1shot" and "Pitch" checked, so if these were the last settings before the sound came out of the sampler, that 808 kick would play the full way thru no matter how short the trigger note was. However, if you look over at the ADSR section you'll notice there's hardly any decay, there's no sustain and no release. So, once the sample has played for that very short amount of decay time, it will be cut off. This is a drastic setting that I entered just to help give you an example, but I am guessing you just need to adjust either the ADSR settings on the front of the samplers, or the "PLAYBACK"
parameters inside the exs24 editor.
If I was able to help, please consider helping me out with a vote in this beat battle on FP:
KFX KICKS BEAT BATTLE#2 - Round#2 - 2 battles - You choose the winner!!!
Lemme know if there's anything else you are wondering that I may be able to help with,
Danarchy