I mostly DJ all the sub genres of house so no oldies sort of stuff usually. I tried analyzing the files with quant and snap on and off. I had Cross DJ free (3.0.1) for a short time but I only analyzed 3 songs on that. Since I am a former Torq DJ user I will use their software to give an example of whats going on:
http://postimg.org/image/n6soyli89/As you can see in the picture, the song has the downbeat right at the drop and then every subsequent 4th beat has another "downbeat". Like I said before most of my songs are 4 on the floor based.
Here is a picture of Cross:
http://postimg.org/image/d23vt3lil/ In this picture, the playhead is right on the downbeat of the song. Cross instead put the downbeat a few measures behind the playhead (I am zoomed in so you cannot see it).
If you need more information I will be glad to provide it.