Any oil paint will yellow over time

Satin Impervo comes in oil or water based. Where I live in Ohio however, oil is no longer carried in gallons and no paint store can tell you how long the quarts will even be on the shelves. VOC laws are taking it away. Your painter that uses water based alkyd is ahead of the curve. I have used 2 SW water based alkyds. Pro classic and Pro Mar 200. They're both fantastic. Much lower VOC. They feel great, look great, and are tough products. Lots of painters just use a water based acrylic on the trim anymore which is fine. Oil will definitely yellow over time. Some oils will yellow a lot. It is still good stuff but it is not by any means above a water based alkyd. You will get a great finish with anything as long as the painter is good. I would let him use what he wants and feels comfortable with using. Especially if they have had good results with it.

I have a BR vanity that was painted in SW Pro-Classics about 4 years ago in Dove White - it has not yellowed at all. Looks like new.

Pro classic is not oil

You are right Christoper! My point was OP should use water base paint.

Yellowing in oil paint is only detectable if the color is stark white-white. If you use cream or darker shades to begin with the point is moot, and the benefits of an oil enamel over ordinary latex/acrylic are plain. Oil will last virtually forever and is the most scrub-able finish.
I said "ordinary"; the new emulsion paints are really great. If you want no-odor/low VOC but still want a hard long-lasting finish, try one of the new formulas like BenMoore's "Aura" line. The finish of their interior gloss/semi-gloss enamels is indistinguishable from Impervo or Dulamel oil-based.
Casey

+ oil is hard to come by most anywhere, except WV for some reason