Even if it is mould (and it may well not be), that is not the end of the world. Checking with a moisture meter will tell you if there is a systemic damp issue, which may mean some damp-proofing work needs to be done. If it is not damp now, that does not exclude the possibility of periodic dampness. Most people, these days, are blissfully unaware of the moisture they put in to the air through breathing, cooking, washing etc. In the past houses were quite well ventilated (usually unintentionally so), but these days people want to save energy by insulating and often end up making their homes hermetically sealed. Bad idea!
So, even if the red colour is due to mould from occasional condensation problems, you can sort that out by ensuring adequate ventilation is in place and/or using a dehumidifier system.