Can you share a screenshot of the facial rigger window? This is my usual setup, but it also needs a post-script to constrain the lips properly.
Pretty old code using pymel, sorry!
import pymel.core as pm
headJoint = pm.PyNode('mouth_0_jaw_Jnt')
# Constrain ALL the lip rope nodes that are under "lips_C_rope" to the headJoint
if pm.objExists('lips_C_rope'):
for each in pm.PyNode('lips_C_rope').getChildren(type='transform'):
pm.scaleConstraint(headJoint, each, mo=True)
# Constrain the corner lip controls to the head control.
if pm.objExists('lips_R_corner_npo'):
lipNpos = [
'lips_R_corner_npo',
'lips_C_upper_npo',
'lips_L_corner_npo',
'lips_C_lower_npo',
]
for each in lipNpos:
pm.scaleConstraint(headJoint, pm.PyNode(each), mo=True)
# Constrain lips_C_crvs to the headJoint
pm.parentConstraint(headJoint, 'lips_C_crvs', mo = True)
pm.scaleConstraint(headJoint, 'lips_C_crvs', mo = True)