Quantized vibrational modes (phonons) of the scaffold has been attributed as a decoherence source to disturb the electronic excitation (exciton) from coherently transfering in a network of quantum subsystems. If the relaxation rate of the phonon to the equilibrium is much smaller than the dipolar coupling of molecules, we show that the exciton transfer is dynamically conditioned due to the temporal Lamb shift and also find that some interesting features of excitonic transfer, such as directionality and quantum walk, are enabled by designing the couplings of the scaffold to the molecules.