The stability of wave conduction in the heart is strongly related to the proper interplay between the electrophysiological activation and mechanical contraction of myocytes and extracellular matrix (ECM) properties. In this study, we statistically compare bioengineered cardiac tissues cultured on soft hydrogels ( kPa) and rigid glass substrates by focusing on the critical threshold of alternans, network-physiological tissue properties, and the formation of stable spiral waves that manifest after wave breakups. For the classification of wave dynamics, we use an improved signal oversampling technique and introduce simple probability maps to identify and visualize spatially concordant and discordant alternans as V- and X-shaped probability distributions. We found that cardiac tissues cultured on ECM-mimicking soft hydrogels show a lower variability of the calcium transient durations among cells in the tissue. This lowers the likelihood of forming stable spiral waves because of the larger dynamical range that tissues can be stably entrained with to form alternans and larger spatial spiral tip movement that increases the chance of self-termination on the tissue boundary. Conclusively, we show that a dysfunction in the excitation-contraction coupling dynamics facilitates life-threatening arrhythmic states such as spiral waves and, thus, highlights the importance of the network-physiological interplay between contractile myocytes and the ECM.