How do hybrid electronic systems work?
The crossbar bus will have some arbitration and communication protocol, such as AMBA for ARM systems. Some of the peripherals will be able to 'bus master' and/or access memory.

One of the processors - usually the most generic ARM - will boot first, from ROM or external Flash. Other parts of the system will be held in reset until they are initialised.

Assigning tasks is the job of the operating system. It's much like the use of graphics and sound accelerators on regular PCs.