Could be a skin infection transmitted from the last person who lay on the bed / table unless it's thoroughly cleaned / sterilised between each use but how likely is that

In a similar way it could be from a skin infection on the girls hands.
A reaction to nut oil or something else in the oil as already mentioned could be the problem or some kind of micro contamination of the oil itself.
Now while I don't think microbes can live in pure oil they can live in any other infusions or water present in the oil, realistically how clean do these girls keep the oils and the containers they use for massage

If they buy a big 5 litre container of oil as it's better value then decant it into a smaller more manageable bottle / jar etc to use during massage how often does the container actually get emptied and sterilised

I'd bet either never or almost never