I've always used soluble oil, and never had any issues with staining, however I am aware there are some that are notorius for causing residue build up.
One big thing to be aware of is soluble oils can be pretty specific for their applications, and I'm guessing that whatever you have isn't suited for brass (some suppliers classify it as yellow metal).

I'm currently running Gulf Cascade HD-S, as it's capable of handling most metals and processes, however the smallest quantity it's available in is 20 litres. The choice for cutting oils in small quantities is very limited, so you either have to run whatever you can find and hope it works, or buy more than you're ever likely to use.