How to prevent unity to deform mesh differently than blender does?

The issue I got for some time is, that unity tends to deform the mesh in a manner where it seems to prevent overlaps of the mesh, which results in ugly looking "hole" on the back in the shoulder-arm-region, when getting the character in a more natural stance than T-pose.

I initially thought it was due to additional bones from rigify, but after rigging it myself it still happens... I can't really figure out what is happening and how to prevent it. :(

Images to illustrate and compare:

Since english is not my native language I did not know what to search for and decided after a lot hours of frustration to just ask other people about it. ;)

Edit: I just looked closly to the image and noticed, that unity made triangles ot of my quadratic mesh ... could it be related to my probem?