When flying diesel engine, you have to trust the FADEC. In fact you have no other choice as it controls the engine.
This seems obvious, but if you're used to the classical three levers (throttle, prop, mix), you will probably feel out of control, or out of the loop, on your first FADEC single lever flights. This impression comes from the way we fly variable pitch props, which has nothing to do with what the FADEC does, because it is so quick and attentive to engine only.
A quick résumé for pilots not used to variable pitch prop:
High RPM for take-off
Slight reduction in climb above safety altitude
RPM reduction in cruise, to have a better engine efficiency
High RPM again on short final, in case of go-arround
With a FADEC, you just select an engine load, in %, and the FADEC decides an engine power and the appropriate RPM. The following diagram is extracted from the DA40D AFM, and shows the relation between engine load and RPM.
This shows that RMP will be maximal at full load, and then decrease, which is quite usual, and then decreases when power is reduced.
But when power goes below 20%, the RMP increases again. For three lever pilot, this means that even at low power the regulator is active, and that moving from low power to no power won't correspond to a prop slowing down !
This feeling is quite strange, and on some approaches in my first hours on diesel, I sometimes put some power back, just to be sure that the FADEC / engine couple was still working properly ! As you can imagine, the results was not exactly a stabilized approach ! I never had any bad surprises during an approach.
An other thing you can expect, is prop pitch change in turbulence, because the wind gusts in the prop will lead to RPM changes, and the FADEC will react to that immediately by adjusting RPM.
To summarize, you have no direct control over prop RPM, which can feel strange, but the gain is that you no longer have to monitor three parameters (MP, RPM, FF), but a single load, with a single lever, so pilot workload is reduced, which is good !