Dependence of the phase and magnitude of the response of Y-Ba-Cu-O edge transition bolometers on the superconducting transition is studied. The responses of both large and small area devices were investigated and several anomalies are observed. The response of small area LaAlO3 devices considerably differed from that expected based on the dR/dT curve. This discrepancy is observed to be strongly dependent on the superconducting transition. Both the phase and magnitude/(dR/dT) of the response of the devices showed abrupt changes for below the Tc-onset when measured versus temperature, while the phase variation also showed strong dependence on the modulation frequency. We present the analysis and propose mechanisms responsible for the modulation frequency dependence of the response characteristics versus temperature, within the superconductivity transition region of the devices.