If you want to split the audio with the video, make sure the audio track is highlighted too. Make sure the channels you want to split are highlighted. To split clips, move the playhead to the points in the tracks where you want to make a split. Then, run Warp Stabilizer only on those shortened clips. To help with this, first identify the shaky portion of the footage and then split the clip to isolate those shaky parts.
Once Warp Stabilizer completes the stabilizing stage, Premiere Pro returns to the normal state. While it lets you continue working in Premiere Pro during processing, it will be a little slower. Warp Stabilizer is a memory-intensive and time-consuming operation.