We study the coevolution of network structure and node states in a model of multiple state interacting agents. The system displays two transitions, network recombination and fragmentation, governed by time scales that emerge from the dynamics. The recombination transition separates a frozen configuration, composed by disconnected network components whose agents share the same state, from an active configuration, with a fraction of links that are continuously being rewired. The nature of this transition is explained analytically as the maximum of a characteristic time. The fragmentation transition, that appears between two absorbing frozen phases, is an anomalous order-disorder transition, governed by a crossover between the time scales that control the structure and state dynamics.