What does the contention-free communication assumption really mean in the context of DAG scheduling?
Not my field of expertise, but I think this is a relaxation in comparison with real-life scenarios. In actual systems, once a connection has been established and a "packet" has been sent (what packet here means depends on the context of the problem being solved), it is possible that an unscheduled interrupt occurs  that pauses this communication and allows a new communication with a different processor to occur.

I believe this relaxation means that once a "packet" is sent, we assume that the other processors do not interrupt this connection until this quantum of information has been sent. Essentially, it makes the processors being collaborators instead of antagonizers and it simplifies the analysis, while still keeping it reasonable, since all processors stick to the schedule and do not monopolize the connection (i.e. they will stop transmitting once this quantum of information has been sent, instead of maintaining their connection and sending their entire message in the expense of others, thus ignoring the schedule given).