Encircling exceptional points (EPs) in non-Hermitian systems has been shown to induce chiral state transfer, whereby the final state of the system is always the lowest-loss eigenstate, independent of the input. When multiple lowest-loss states coexist, it is generally expected that EP encirclement yields mixed outputs composed of these states. Here we reveal a distinct regime, peculiar of non-Hermitian systems hosting multiple iso-imaginary Riemann surfaces, extending the conventional understanding of EP dynamics. We find that states residing on higher-loss Riemann surfaces preferentially undergo nonadiabatic transitions to the nearest lower-loss surface, while transitions between iso imaginary surfaces are strongly suppressed. This fixed-selection-rule dynamics enables input-state-dependent chiral transfer, such that encircling the same EP produces distinct and well-defined output states for different inputs, rather than mixed output states. We experimentally demonstrate this mechanism in a photonic platform, revealing new EP dynamics beyond conventional chiral state transfer, and opening a pathway towards mode-selective, high-capacity non-Hermitian photonic devices.