  We consider the exact time-evolution of a broad class of fermionic open
quantum systems with both strong interactions and strong coupling to wide-band
reservoirs. We present a nontrivial fermionic duality relation between the
evolution of states (Schr\"odinger) and of observables (Heisenberg). We show
how this highly nonintuitive relation can be understood and exploited in
analytical calculations within all canonical approaches to quantum dynamics,
covering Kraus measurement operators, the Choi-Jamio{\l}kowski state,
time-convolution and convolutionless quantum master equations and generalized
Lindblad jump operators. We discuss the insights this offers into the
divisibility and causal structure of the dynamics and the application to
nonperturbative Markov approximations and their initial-slip corrections. Our
results underscore that predictions for fermionic models are already fixed by
fundamental principles to a much greater extent than previously thought.
