What version of JMP are you using ?
I tried doing something similar in version 12.2, and the columns are saved to the summary table as I expected.
This is what I did :
dt = open("$Sample_Data/Big Class.jmp");
dtsumm = dt << Summary(
Group( :age ),
Mean( :height ),
Mean( :weight ),
);
obj = dtsumm << Bivariate(
Y( :Name( "Mean(height)" ) ),
X( :Name( "Mean(weight)" ) ),
Fit Line( {Line Color( {208, 64, 86} )} )
);
obj << (Curve[1] << Save Residuals);
The residuals were saved to the summary table as I expected.