It almost sounds like a sustain pedal 'polarity reversal' kind of thing, but since you are not using a sustain pedal that makes it confusing.
Do you HAVE a sustain pedal plugged in, but just are not stepping on it? If that is the case, it could be that the polarity of the sustain pedal makes it such that 'off' is interpreted as 'on'. This is often called a 'polarity' issue, and it happens because of differences in how one set of manufacturers decided what means 'off' for a sustain pedal, versus 'on', and another set of manufacturers implemented THEIR sustain pedals to be the exact OPPOSITE.
So, IF you have a pedal plugged in, but are not actually stepping on it, perhaps you could either try stepping on it during playback to see if that makes it sound correct (confirming a polarity issue), or you could try simply unplugging the sustain pedal and see if that fixes it.
If you DO have such a polarity issue with your sustain pedal, many keyboards and midi controllers have a function that tells it to flip how it sees sustain pedal off/on signals, and that should take care of it.
I hope that helps,
Bob Bone