Oil wiping stains are easies to tint. Laquer stains can be tinted, but it takes an HVLP to do it well, and even then you can still see some of the spray pattern at spots. What you do is take a piece of that cherry cabinet and a piece of the poplar trim to the paint store and have them match the stain. You're only looking for the right color family. As long as it's close you can tweak it.
When you get your stain to the jobsite, if you're using oil wiping stain, open the can and let it breathe a little bit to get rid of some of the thinners in the stain. Run it through your rig, and spray it on a sample board, nice and even. Then, with a dry brush, stand over it and wait till it just starts to dry out. Now brush with the grain taking off only as much stain as needed to lighten the coverage to get to the right color. Now brush against the grain with just the tips of the brush, then with the grain with just the tips of the brush (rag out the brush as necessary). Work it until the stain doesn't pull back from the grain features (knots etc). Once that stain is thick enough, it will stay right where you put it.
Work one board a few times and you'll get the hang of it. It's not that hard. Just make sure you don't leave a piece of trim too early.
Poplar is actually pretty easy to get really dark. It's got a nice porous grain that accepts stain pretty easily. If you need it really dark, you could try wetting your trim down and pre-sanding to raise the grain up a little bit. Just use a damp cloth and run it over your trim, then sand by hand w/ 100 grit and long strokes. It'll open up that wood and let the stain penetrate much better. Just make sure you sand it all.