When scaling the root bone of a rig to apply a global scale, the corrective smooth modifier results in wrong deformation due to incorrect scaling.
The delta calculations are not taking into account any scale value.
To fix it, a scale property is added to the modifier, allowing to set manually the scale value for the deltas by simply multiplying the vectors by this value.
There is a similar implementation in Maya's Delta Mush deformer. This property can be for example driven by the scale of the root bone of the rig, to dynamically update when the animator scale this bone.
It seems to work as expected after some tests, however one (small) issue I can't fix for now is this new Scale value is set to 0 when opening older file with objects having corrective smooth modifiers. It's properly set to 1 as default value for newly created modifier. I'd be glad to get support from any experienced developer to fix it.