Most likely, if Ableton Live’s clips are not playing in time, your samples are not properly warped. They may have a leading silence at the beginning of the clip. An easy way to get around this issue is to go into Ableton Live’s preferences and disable “Auto-Warp Long Samples,” which is located in the Record, Warp, Launch tab of Live’s Preferences. Retrigger your clips again and see if this fixes the issue.
If your clips are not properly launching in time and you want to keep your clips warped, go to each track and make sure that there isn’t leading silence at the beginning of the clips. If there is, zoom into each clip as much as possible and move the start clip flag right to the very beginning of when the audio sample actually starts, then right-click and select set 1.1.1 here, then right click once more and select “Warp From Here (Straight.)” Then retrigger your clips.
Also, by default all clips will launch according to the global launch quantization setting (located at the top left of the screen to the right of the metronome) Quantization is used to avoid rhythmical error when playing clips. To set specific clips to trigger on a quantized value separate from the global quantization, select a clip (midi or audio) then click the L in the Clip box (the skinny box located in-between the help/info view and the sample or notes box), then select the desired quantization value in the pull down menu (again Global is the default).