Stains on underlayment and roof beams

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The process after the shell construction is such that the roof is completed first before steam or condensate occurs.
So also before the windows, ensuring that moisture can ventilate through masonry or concrete work beforehand.
(The windows and doors usually also have delivery times.)
If the attic space were not a heated living area, the thermal envelope would be constructed incorrectly.

I have encountered such a case before, where with an insulated top floor ceiling the vapor barrier under the wooden ceiling was missing.
Mold formed on the foil as well as on the beams. Cleaning only helped visually, because the foil had pores for water vapor diffusion.
The agent penetrated the pores and the joint between the foil and the rafter did not take effect. (The rafter was wider than the base battens)
Since mold kept reappearing, the foil was later replaced.

The process was the same for us, with the roof coming first (October 2020), then the windows (November 2020), then the plaster (December 2020), and later the screed (January 2021) was installed in the house. I suspect that the mold appeared after the screed because, according to the screed installer, we were not allowed to enter the house or ventilate for 7 days. The mold on the underlay membrane can almost be wiped away. However, I have treated it and the beams with a mold remover anyway.

Since the roof is insulated, it is the boundary of the heated envelope to a living space. The roof is only considered complete here when the insulation and the vapor barrier have been installed. The interior finishing, such as heat protection, can be done later. By the way, this also makes the work easier, as the insulation does not have to be installed overhead but can be placed on the vapor barrier before roofing.

I don’t understand. The sequence is: installing the roof beams and ridge, underlay membrane, roof tiles, insulation, and then the vapor barrier.

How the individual steps are carried out does not matter and depends on the weather. It makes sense to have the vapor barrier against water vapor from the inside. There should then be no condensation through the insulation. Otherwise, only thorough ventilation of the attic helps.