Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing general collective patterns behind spatiotemporal 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 spatiotemporal co-occurrence of individuals. The rank-size distributions of dynamic population of locations in all unit time windows are stable, although people are almost constantly moving in cities and hot-spots 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 spatiotemporal 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 "inactive" state, people are scattered in smaller communities. Above discoveries are universal over three cities across continents. In addition, a city stays in an active state for a longer time when its population grows larger. Spatiotemporal interaction segregation can be well approximated by residential patterns only in smaller cities. In addition, we propose a temporal-population-weighted-opportunity model by integrating a time-dependent departure probability to make dynamic predictions on human mobility, which can reasonably well explain the observed patterns of spatiotemporal interactions in cities.