Lithium niobate waveguide arrays (WGAs) offer rich possibilities for all-optical shaping, switching, and routing of short optical pulses. In such systems, light from the fundamental wave (FW) is coupled by the χ(2) nonlinearity to the second harmonic (SH) giving rise to a strong cascaded quadratic nonlinearity. Recently a new type of phase transition in the nonlinear localised states was identified due to the competition between self focusing and SH waveguide coupling, where the SH phase profile abruptly switches from in-phase to staggered structure as the input power is increased. However, the temporal extent of the short laser pulses used in realistic experiments leads to a complex pulse reshaping in the course of propagation. Never studied experimentally before, such temporal dynamics is important for utilising the phase transition phenomenon for applications in optical switching. In this work, we study the spatio-temporal dynamics of pulses in lithium niobate WGAs and describe numerically and characterize experimentally the complex spatio-temporal nonlinear pulse transformations associated with the phase transition.