It sounds like the samples have been exported from Pro Tools with “dead air” after the sample content. Have you checked the files in an editor other than PT?

If you’re importing into Rytm, I would cut the lead in down to nothing, so the file begins as close to the start of the sound as you can make it. The Rytm’s start point settings are not very fine grained: you’re limited to 120 start points across the length of the sample. For one-shots, you’re best of trimming to just the audio content.