If you follow this and other similar mattress marketing back, it leads to a product called Purotex made by Bekaert Textiles. They have a promotional leaflet which has clearly been supervised by lawyers checking against laws which restrict health claims. The leaflet says:
Probiotic bacteria and textile products containing probiotic bacteria
are not active substances or biocidal products within the meaning of
Biocidal Products Directive 98/8/EC, as they exert no action against
harmful organisms. Instead, these bacteria consume the excrements of
dust mites that are known to contain several allergens, causing
uncomfortable conditions to humans. There are no intended (claimed) or
known unintended biocidal effects as regards the use of probiotic
bacteria or textile products containing such bacteria.
The Probiotic Task Force members are committed to ensure that statements, e.g., in marketing materials, the press or elsewhere are clear, consistent and not misleading for the users of their products.
So they seem to claim that it could reduce allergens from mite excrement, but seem to deny claiming that it "eats germs".