the airflow is surely due to the suction movement of the pistons, but I think you are mistaken on how the fuel is taken in, the fuel is injected when the piston is at the top of the combustion stroke into the fiery hot airball either in the precup or the piston dish itself (depending on DI or IDI) which causes the burn to happen. The fuelling is controlled by the pedal position and the engine rpm, so if you mash the pedal at high gear in low rpm your engine will not smoke hard by overfuelling, but offer the max fuel for that given pump rpm.
Some overfuelling was built into old diesel pumps to keep the power up but only on full fuel, this power was cut down when the rpm governor opened up compressing the metering sleeve in a VE pump or stopping rack travel in an inline pump. Modern diesels are operating on direct injection with piezo nozzles to inject upto 5 strokes of fuel to quiet down the noise and to tune the power band. But the basic operating principle is the same.
You might see some diesels today with assemblies that look like throttle blades, those are placed for EGR to function and they also boost blowby suction into the intake, In some engines they are also used to tune the intake tract.
Some older engines had throttle blades to control manifold pressure, manifold pressure was then relayed to the pump to increase fuelling. Such engines belch really thick smoke when not in tune, and are a general PITA to keep up with.
