Your circuit might be linear, but if you run time domain simulation using S-parameter (frequency domain!) data, that involves heavy math behind the scenes to do the FFT. Your input to the FFT is only narrowband data plus DC, so I would not expect accurate response in time domain, even for a linear circuit.
If you want to EM only narrowband, and your device is linear, you should use S-Param simulation. That is valid because it only requires the actual frequency range used in S-Param controller, and does not need convolution/FFT.
Best regards
Volker // Keysight Certified Expert EDA