I haven't gotten to Milfy City yet, so I haven't seen the animations, however there are a number of potential options.
First, there morph packs for Daz that allow you to alter the shape of glutes and breasts (example:
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) Judicious use of those can create some of these effects, since there are things like "shift up/down," "squeeze," "impact," etc. in many of the morph packs. By changing the morph setting from frame to frame you can simulate some softbody effects during the course of an animation.
As for "fingers pressing into things," one way you can probably do it is to use Daz's "Smoothing Modifier." It's primarily intended for getting clothes to fit better, however it essentially does some collision detection and mesh warping. In normal use, you add a Smoothing Modifier to clothing and set the collision target to the figure wearing it. The Smoothing Modifier will then detect "collisions" (i.e. places where the figure pokes through the clothing) and try to warp the clothing mesh to un-collide (i.e. get the clothing outside the figure's mesh.) If you were to add a Smoothing modifier to the figure being spanked/fondled and set the collision target to the figure that owned the hand, you could probably get a "breast/butt indents away from the fingers" effect. Since the collision detection moves the mesh only just enough to avoid the collision, you'd get different amounts of "indent warping" based on how much the two meshes intersected, which, of course, could vary frame-to-frame.
Another way to alter a mesh is to use a D-Former. You can specify an "influence area" (either by resizing the D-Former's "spheriod" or by painting a weight map) and then use it to warp the position of the vertices in the mesh. I've used this for things like "make the sheet and mattress indent where a figure has his/her knee," for example, or to create "he's erect inside his pants" bulges in clothing. Again, the amount of deformation can be changed frame-to-frame.
Last, but not least, you can create your own morphs using Blender or another modeling tool. You export the mesh, typically as an OBJ, shift vertices around, and then re-import the mesh using Morph Loader Pro. This then gives you a "morph dial" just like any of the other morphs in Daz. (This is, in general, how they're created.) And, like any other morph, you can alter it's amount frame-to-frame.
I obviously don't know how ICSTOR actually did the animations, but those are the common techniques.