What do you mean? Are you asking how to apply textures or colors to your model in 3dsmax? If so, you use the Material editor, I think the shortcut is still M.
If you mean the painted colours, I haven't tried with Max yet but I'm guessing it follows the OBJ format correctly. Medium kind of cheats, it saves colours as 6 dimensional vertices (it joins position and colour together). This is actually not part of the official OBJ format spec and a lot of software won't support it (either ignore it or fail).
Meshlab does support it and can convert, so there might not be an easy alternative to using it.
What do we need to ask exactly from 3ds Max to support this formats? Is there a specification to this format that they could look at to support? It's really annoying going through Meshlab for this.
The problem is Max is doing things correctly. OBJ is the wrong format for vertex colours, Medium should have used a format that officially supports colour like PLY (it's easy, text based and supported by most software).
Neither Blender, Max or Maya support OBJ files with colours. (And it was one of Maya's founding companies that invented the OBJ format).
OBJ is pretty simple though, it wouldn't be overly hard to write a max script (painful, because maxscript sucks, but not too hard) that reads the non standard medium version of obj.
I don't use 3DS Max but I use Maya, if I convert the obj in MeshLab to a .dae file format it works in Maya when I import it and turn on vertex colours.
I followed this, hopefully the same will work for Max: https://forums.oculus.com/community/discussion/45883/how-to-export-vertex-colors-into-maya#latest