Phase edit help in Ableton vs Pro Tools

I have both DAWs and I'm slightly confused about making phase edits. I know how to use them both, and solidly know the concepts behind phase edits, but something is different between the two programs and I'm not sure if it's a setting I have on or "that's just how it goes". Here the scenario:

I am trying to make a phase edit of a song to isolate each instrument to it's own loop. The intro has a synth in it for a few bars, then in comes the drums. I have been able to successfully cut the synth intro, and move it to a second track below the drum + synth part and I get just the drums... ONLY if I do it in Pro Tools. If I do the same in Ableton Live, with the track unwarped, and the grid off, I notice that the waveform is somehow not the same throughout. In Ableton Live, the first synth hit is exactly lined up, but the second one will be slightly off.

I hope that makes sense. My question is, how do I make Ableton stop doing this odd warping so I can make these edits in that DAW, as Pro Tools is unstable and slow.