Are you talking about getting the dye down into to grain lines and you are seeing little white lines? This is very common with Red oak and less with White but I've seen it.
You were on the right path with the detergent. It is a surface tension problem. I assume you are using a water based solution of Analine if you were adding detergent.
One idea might be to try an alcohol based solution. Harder to work with but depending on the form of the piece might be better.
The other thing (that I do with water based stain on Rad Oak) is to scrub it in. You need to get a stif bristle brush and actually scrub it into the grain. Go both against, with the grain and in circular. You aren't necessarily getting the bristles into the grain, just breakling the surface tension soi it can flow in on its own.
I've also found when using NGR type Analine pre-mixes that flooding the surface gives a much better color than just dainty application.