We propose a control synthesis framework for a heterogeneous multi-robot system to satisfy collaborative tasks, where actions may take varying duration of time to complete. We encode tasks using the discrete logic LTL^ψ, which uses the concept of bindings to interleave robot actions and express information about relationship between specific task requirements and robot assignments. We present a synthesis approach to automatically generate a teaming assignment and corresponding discrete behavior that is correct-by-construction for continuous execution, while also implementing synchronization policies to ensure collaborative portions of the task are satisfied. We demonstrate our approach on a physical multi-robot system.