This Ableton tutorial demonstrates how warping works inside the Simpler device, showing that samples stay locked to your Live Set's tempo automatically. A drum loop is used to illustrate the point: as the session tempo changes, the loop adjusts in real time without drifting.
The same sync behavior holds when you play the sample at different pitches from a MIDI keyboard. Pitch-shifting through Simpler doesn't break the tempo lock, which means you can use a single warped sample across a range of notes without losing rhythmic coherence.