Generating histograms from a fitted pdf in RooFit

Dear RooFit experts,

I perform sideband fits to a RooDataHist using a RooExtendPdf.
When plotting the fit result the VisualizeError option shows the uncertainty of the fit.
From my sideband fit I build a template RooDataHist with the generateBinned() method.

Now I have a rather general question:
I would think that the uncertainty on each bin in the template RooDataHist should be determined by the fit uncertainty. If I am right, is this taken into account by the generateBinned() method or are the bin uncertainties only represented by the Poisson uncertainty on each bin?
Is there a possibility that I can implement this in my code?

Thank you for your help in advance.

Best regards,

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