I prefer to keep my detergent at neutral - even with poly. Poly is oil loving so you need something to break up that bond. A neutral upholstery prespray boosted with a water soluable solvent booster(Prochem's Citrus Pro, Bridgepoints Citra Solv, CTI's Citra Quick - pick one). For poly that has a lot of spills I add an oxy booster(Bridgepoint's Boost All, Steamway's OBB, Prochem's Oxy Plus - pick one).
Apply your prespray EVENLY - agititate with a horsehair brush. Take some terry towels and begin cleaning the "touch points"(arm rest, cushions, back, head rest, front skirt). Then rinse with your upholstery tool of choice. I like to follow up with a terry towel after rinsing. It helps remove a small amount of additional soiling as well as dry the piece faster. Put an airmover on it to dry it quick.
I don't recommend prespraying the WHOLE piece at once, work in smaller sections. Also if you're working with microfiber, be sure to groom the piece with your horsehair brush - brushing the "pile" of the fabric all the same way.
Of course test any products you use before applying to the whole piece, but as Kevin said its hard to hurt a poly upholstered fabric(it can be done though)