With my Galaxy S3, my girlfriend's Galaxy S4 and her mother's Galaxy Core, we cannot download MMS automatically. We have to turn on data before doing so.
This problem is not happening with her sister's Galaxy Ace: whenever they receive a MMS, data is automatically turned on, and then off once the MMS is downloaded.
Now, this isn't a real problem most of the time (more of an annoying one), but my girlfriend's mother has a very low data plan (100mb) and often forgets to switch off data once the MMS is received, so she often maxes out her data plan.
I have tried something I found here: copy the existing APN and setting only "mms" as APN type, but it doesn't work.
My girlfriend and I are Orange (France) and her mother is Bouygues.
Thanks for your help!