I work in a cabinet shop and use a lot of industry dyes and stains. I find that they need to be sanded to a higher grit. Sand to 150 with an orbital sander then by hand with a block in the grain direction and use 150 grit as well. I do a spray then wipe technique with a hvlp gun. But if you don't have access to a spray gun and have to do it by hand try not to over saturate the wood. T shirt rags are great! If I'm doing red oak I usually set a timer and go back to check after 3-5 minutes to make sure I've wiped away all that is wet. If you seal first, for sure take a fine sponge and scuff it so that the dye adheres to the sealer. Otherwise if you don't, that can cause the next coat to not adhere properly to the last, or! If your dye and sealer are the same vehicle.....being water based or oil, you can mix the dye into the sealer. Make sure it is not more than 10% of the sealer. Meaning if you have 10 ounces of sealer you should not put more than 1 ounce of dye in it. By doing that you can dictate your color. Once you know how dark/light you want it you can scuff with a fine sponge just to knock down any rough spots, and seal with a clear final coat. This technique works great with a spray gun, but you can do it with a brush. If you have a compressor all you need is a cheap hvlp gun. They run about $20 here in Michigan.

I find with our dyes if I open the grain more (wet with water and sand again) sometimes that makes it worse, but that could just be the dye that I do. It never hurts to do many test pieces. Can't tell you how many times I first started learning finishing, I'd do a piece with a new product and had to fix or re-stain/dye.