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Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are still lacking a comprehensive understanding. Massive cellphone data enable us to construct interaction networks based on spatio-temporal co-occurrence of individuals. The rank-size distributions of hourly dynamic population of locations are stable, although people are almost constantly moving in cities and hotspots that attract people are changing over time in a day. A larger city is of a stronger heterogeneity as indicated by a larger scaling exponent. After aggregating spatio-temporal interaction networks over consecutive time windows, we reveal a switching behavior of cities between two states. During the "active" state, the whole city is concentrated in fewer larger communities; while in the "sleeping" state, people are scattered in more smaller communities. Above discoveries are universal over diversified cities across continents. In addition, a city sleeps less, when its population grows larger. And spatio-temporal interaction segregation can be well approximated by residential segregation in smaller cities, but not in larger ones. We propose a temporal-population-weighted-opportunity model by integrating time-dependent departure probability to make dynamic predictions on human mobility, which can reasonably well explain observed patterns of spatio-temporal interactions in cities.