Gimbaled thrust is common in modern SAM and AAM systems.
It would tilt a little, but the general idea is that the nozzle does the tilting while attempting to keep the missile as straight as possible
An example of what we are seeing at Whidbey can be found at 2:33 in this video, with the long exposure of the Whidbey frame creating the appearance on the photo of the long rocket tail.
https://www.youtube.com/watch?v=JcB4eJ6lHOY