Active mold (mold being a non-scientific reference to any manner of
fungi) requires moisture to start and thrive, and it is obtaining that moisture from your breath during inflation! Moisture + Warmth (from lying on the mat...). To mold, the dark insides of your mattress/es is a most appealing place to be!
It is possible (but
not a rule) to pick up a bacterial infection or an allergy if in contact with a lot of it repeatedly. Mold spores are
everywhere around you, but to become a nuisance they require moisture, in which they will proliferate, which is why you can find mold hiding behind bathroom mirrors, along the eves where moisture rises et al. If there are a large number of mold spots or they are increasing, it is better to discard the mattress — I cannot imagine trying to eradicate it by continuing to use it, rather the opposite of encouraging it to thrive.
Concentrating a spray of
Glen 20 through the inflator and then sealing the valve may have a small affect; you'd also do this when selling your mattress to another user. Glen 20 is effective against many types of fungi, viruses and opportunistic pathogens e.g.
e.coli,
pseudomonas aeruginosa, which gather enthusiastically around toilets, wet basins, baths and sink areas. Bleach is a powerful remedy (used in hospitals against MSSA and MRSA (both are 'golden staph'), which don't care much for ordinary antiseptics), but don't put that into a mattress.
Take-away: replace the mattress.