Bad staining to relatively new stucco on home applied over siding

Hello. I have a 4000 sq ft home in So CA desert. I had 3 stucco contractors come to give me bids since the siding (a type of fiber board) was warping and coming apart due to the hot dry summers and cold wet winters after 20 years. Since most of it was still in relatively good shape, 2 of the contractors recommended I leave it in place for insulation value, and stucco over it after wrapping the house in two layers of paper. My concern is that I have a lot of staining happening to the stucco now after a few rains (this was completed last summer). It hasn’t rained for weeks, but you can see the staining in the photos. No idea what has caused this, or if it is normal? Some parts of the house the walls have no staining at all, whereas other parts, where water seems to run over the surfaces off the of the roofs/decks, the staining is severe. I have the contractor coming tomorrow to look, but quite honestly, based on the job and how it went, I really don’t trust what he might tell me. Any qualified opinions from those in the industry would be greatly appreciated!! Thank you