Element specific ultrafast demagnetization was studied in Fe$_{1-x}$Ni$_{x}$ alloys, covering the concentration range between $0.1<x<0.9$. For all compositions, we observe a delay in the onset of Ni demagnetization relative to the Fe demagnetization. We find that the delay is correlated to the Curie temperature and hence also the exchange interaction. The temporal evolution of demagnetization is fitted to a magnon diffusion model based on the presupposition of enhanced ultrafast magnon generation in the Fe sublattice. The spin wave stiffness extracted from this model correspond well to known experimental values.