How should I make a club music transition from 130bpm tune to 90bpm tune, and vice versa? I want it to be as seamless as possible. I have tried simple cutting, but that does not seem to be really the quality way to do it. How do the pro DJs do it in the clubs as they seem to be able to always make the transition smoother than I have been able to?
This is a matter of taste more than a technical issue, so I'll be using terms like "groove" and "feel" rather than more quantifiable criteria.
It comes down to making it seem natural instead of jarring.
Since you mention club DJs, I presume you mean "in front of dancers," and the human body is going to move differently at 90bpm than it is at 130. A simple cut goes from one movement to another with no signalling and a clear juxtaposition, so it will take the dancer some time (a measure or so) to pick up on the new groove.
There isn't a clear always-works strategy, but you can put tools in your toolbox to practice and use as the situation fits. Here are some examples:
A rhythmically ambiguous section between the two tracks. Mix from the first track into an atonal or aryhthmic breakdown recording, and then mix the new track in from that. This will obviously depend on your genre and situation.
Mix from the old track into a spoken-word (not ryhthmic) intro on the new track. 90bpm is right in hip-hop's range, and you see this sometimes in that style.
Signal the new tempo somehow. I have had some success with building up the old track using a delay effect set to 1/4 or 1/2 notes at the tempo of the incoming track. It sounds like a dub delay on the old track, which is kind of weird but not "wrong" sounding, and as you disappear the old track into a wash of echoes, the new track can come in in time with the new groove timing you've been hinting at. I've had more luck with this going to increasing speeds, but your mileage may vary.
Don't beatmatch at all, just fade the old one out and fade the new one in, radio-style. Obviously this will be a bit odd if you're trying to make a seamless set, but it can work depending on context.
These are just ideas to try though; what works for you will be very dependent on your style and sensibilities, it is probably worth finding examples of other DJs making similar transitions in your style, and analyzing what they do and why it works. A good question, when playing dance music of any sort, is to ask "could I dance to that?" In the end, your goal is to entertain.