We investigate the dynamics of liquid emptying from hydrophilic cuvettes with square cross sections, focusing on the role of surface tension, cuvette dimensions, and tilting rate. While the static deformation of menisci is well-studied, the transient behavior during tilting—relevant to practical scenarios such as pouring and accidental toppling—remains limited to some theoretical studies only. Experiments with aqueous solutions of varying surface tension, achieved via surfactant addition, reveal that lower surface tension accelerates the advancement of the contact line and facilitates meniscus deformation. However, body force as a combination of gravity and centrifugal force plays a significant role in fluid redistribution in the cuvette, altering the spilling dynamics. Mapping these regimes for hydrophilic surfaces uncovers non-intuitive behavior not captured in prior studies. Notably, a stagnation phase is observed at moderate surface tensions, where capillary and gravitational forces balance, resulting in no net acceleration of the advancing meniscus. At extremely low surface tension, rapid interface deformation drives continuous acceleration. Furthermore, increasing cuvette size enhances the likelihood of spontaneous spilling, while unexpectedly, higher tilting rates can suppress spilling due to insufficient time for lateral spreading. The study provides a comprehensive force balance and regime map, elucidating the roles of surface tension and tilting dynamics in transient meniscus behavior. These insights are valuable for the design of open-ended microfluidic systems, industrial pouring processes, and biomedical devices where precise control of liquid transfer is critical.