The default option in forecast with covariates method is xreg+timesfm. The docs mention that:
'xreg_mode: one of "xreg + timesfm" or "timesfm + xreg". "xreg + timesfm"
fits a model on the residuals of the TimesFM forecast. "timesfm + xreg"
fits a model on the targets then forecasts on the residuals via TimesFM.'

However, the function is implemented the other way around.

See L488:494 and L

if xreg_mode == "timesfm + xreg":
# For fitting residuals, no TimesFM forecast on the first patch.
train_lens.append(max(0, input_len - self.input_patch_len))
elif xreg_mode == "xreg + timesfm":
train_lens.append(input_len)
else:
raise ValueError(f"Unsupported mode: {xreg_mode}")

And: L537 to 585.