that's a pretty complex effect and honestly not one that would be accomplished easily in Maya
I've created a similar effect using particle expressions that drove the UV placement of particles leaving trails of particles on a goal surface. Then using blobbies and scaling the particles you can get these tendril like shapes.. the problem is that if you want the goal surface to deform then have the particles in the trail stick to it is incredibly slow and also the particle count goes through the roof for a simulation like this. So if you don't die of old age waiting for it to do it's work you'll probably run out of memory.
There might be other ways to fake but to get the same gooey look you need the blobbies which means lots of particles which means trouble in Mayatown.
Although another possible solution in Maya instead of using goal objects is to create your particles in more or less a 2d plane, then add a plane as a wrap deformer and then shape and animate that plane to match the surface you are transforming. This will help with the slowness but you'll still probably run into memory issues if you want any level of detail.