The problem is caused by QuickTime decoding. MJ12 uses installed external decoding software for decoding m4a audio files. If it uses Apple's QuickTime also the used playback engine is external (it uses the QuickTime player engine) and it is not possible to redirect the decoded output to MJ12 for burning audio CDs.
However, it is possible to use an alternative decoding method. MJ12 can use an installed DirectShow filter for splitting m4a container files and decoding the included audio streams. When the DirectShow method is used the decoded audio stream can be routed back to the internal engine and Audio CD burning, DSP features, visualizations, and format conversions become available.
You would just need to install a suitable filter or filters. In my experience the best DirectShow filter for handling m4a audio files is the DC-Bass Source Filter. It contains the two needed components in a single filter (splitter and decoder) and it can decode many kinds of m4a files (AAC-LC, AAC-HE and Apple Lossless).
It is freely available from the developer's site:
http://www.dsp-worx.de/?n=15I just tested the filter again and it works fine for me without any changes in MJ12's settings, but if just installing the filter doesn't not cure your problem automatically we may need to do a couple of additional steps in order to make MJ12 aware of it.