Characterization of such microwave signals with a method extendable to an arbitrary number of temporal modes with a single detector and demonstration of their phase-robust nature are of great interest. Here we show the on-demand generation and Wigner tomography of a microwave time-bin qubit with superconducting circuit quantum electrodynamics architecture. We perform the tomography with a single heterodyne detector by dynamically changing the measurement quadrature with a phase-sensitive amplifier independently for the two temporal modes. By generating and measuring the qubits with hardware lacking a shared phase reference, we demonstrate conservation of phase information in each time-bin qubit generated.