Your issues relate to some advanced AE thingies such as Render Pipeline and how Distortion Effects work with Collapse Transformations/Continuously Rasterize (CT/CR). There is a lot written about the Render Pipeline, so you should find ample info there.
There is however very little written about how distortion effects with position parameters are affected by CT/CR. For such distortion effects, their position parameter refers to (is relative to) the layer size and not the size of the comp. If you apply CT/CR to a layer with such a distortion effect then the effect's position parameter becomes relative the size of the comp it is in - hence the change in the values.
What you should do to alleviate this problem is to scale up your AI layers and switch on CR in a lower level comp (child comp). Then nest these layers into a 'final comp' where you do not need to apply CT/CR. Then apply the required distortion effects onto the layers in the 'final comp'. Hope that makes sense.
Lastly, for what you're doing, there is a very good chance that the Puppet Tool will be a more functional solution than either of the distortion tools.
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