I would be surprised if an ultrasonic cleaner will remove slight surface rust, or lime-scale which I assume is what is in the injectors. They are really for removing grease and similar contaminants, and particles adhering to the grease. They might clear water-treatment residues (tannin) from boiler-fittings though.
I would advise cleaning the air-brush in the appropriate solvent first, not relying on just the ultrasonic bath. Use that for a last rinse.
The cleaner manufacturers will advise on what additives, but naturally will almost certainly recommend the ones they sell! However, as I recall from work, the normal additive is basically a detergent with a pH-adjuster making it slightly alkaline, so as Andrew suggests, ordinary washing-up liquid will probably work as well as any.
You may also see advertised, second-operation rinse-aids for these cleaning-tanks, but I doubt we'd need these for our processes. They are for very fine surface-preparation such as prior to using specialist adhesives.
I would not use vinegar for grease-removal. A mild alkali such as detergent or washing-soda is better for that. (Hence all that present advice about washing our hands with soap and water!) It is also a bit kinder to ferrous metals than an acid.
Acids will go for lime-scale, but be careful not to pickle the injector cones and valve-seating themselves.
Some of these cleaners also heat the water, making the action more efficient.
I would not put the items in a solid-walled beaker either, unless by advice or suggestion in the machine's own operating-manual. A thin-walled container made of plastic of similar density to the fluid might be OK, but otherwise any container not matched acoustically to the bath will simply reflect lot of the sound back off its outer surface, and heavily attenuate any that does manage to penetrate the wall. A beaker will only help handling the work-pieces, but hinder cleaning them.*
Use the work-basket supplied with the cleaner, suspend the work on thin wire or string, or just lay it on the tank floor – and never put your hands in the water when the tank is running.
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*(This matching necessity explains the gel used in a medical ultrasound scan. It prevents an air-gap between transducers and skin, and helps the sound to pass with minimum attenuation across the boundary caused by contact between materials of different densities and sound-transmission speeds. The scan itself is detecting the echoes from similar acoustic boundaries within the body.)