The bone causing the twitching is the first def bone of the tongue, which is a 5-segment bendy bone that gets roll-in and roll-out from its parent and child respectively. But its parent and child have rolls pointed in almost opposite directions, meaning that the rest pose of this set of segments is actually rotating through almost 180 degrees.
We'll enable the display of bone axes (almost always a good idea when working on a rig) and switch the display to bendy bones, since those are what we are working with and we need to see what they're doing. (Custom shapes, bone colors, stick display, etc-- all that is for the animator, and while rigging, those are only going to obscure information that we need to identify and fix issues.)
The roll is an angle, read only in the -180 to 180 range, but because that angle is distributed over 5 segments, there is a very big difference between -179.99 and +179.99 degrees: -180 is the same as +180, but some fraction of -180 is not the same as that fraction of +180. Since it is basically 180 degrees to begin with, tiny imprecisions can lead to it flipping which angle it's seeing, and we see that just moving the root sometimes leads to the pose shown at right.
If we align these bones' axes, it'll stop having a "rest twist" on this bone. Because the child is also a bendy bone, and we don't want to screw up its roll either, we'll do this by setting the roll of its parent, "Ultimate_tongue_rig", to 180. When we do this, the rest twist disappears and the tongue stops twitching when we move it.