The temperature dependence of the spin-lattice relaxation times (${\mathrm{T}}_{1}$ ) of $^{23}$ Na and $^{11}$ B nuclides has been studied in a number of Na-borate and -germanate glasses and liquids in order to understand the effects of the type of network, concentration of the modifying cation, and network former-modifier interaction on the transport of Na cations. Our results indicate that at low alkali contents the dynamics of both the network former and the modifier are strongly coupled to the glass transition and mixed alkali effect on spin-lattice relaxation is absent. This can be explained by the lack of any percolation pathway at low alkali concentrations for the long-range diffusion of the Na cations. Eventually, such continuous pathways for diffusion form with increasing Na concentration (${\mathrm{Na}}_{2}$ O\ensuremath{\geqslant}15\char21{}20 mol %) and a mixed alkali effect becomes observable, indicating decoupling of the dynamics of the network-former and -modifier ions. Simulation of the ${\mathrm{T}}_{1}$ data with a barrier height distribution model also indicates such a transition from homogeneous to percolative transport with increasing ${\mathrm{Na}}_{2}$ O content. These phenomena are less pronounced in germanates than in borates, indicating a stronger coupling between the Na ions and the network in the latter.