Just so I can understand.
How did you decide that the belt needed to be replaced? Was it shredded? Loose? Showing signs of wear? Something else completely?
How did you remove the first belt? Were you having any issues prior to removing the belt? Are those issues the same now as before?
In my experience - overtightening can cause just as much issues as under tightening. Do you have a set of drawings and manuals for your machine? I am assuming you have a technical report from PSI for it - which should include these things, and things like type/style of belt for replacement, as well as, type/size for the bolts and tension and what not.
I only worked on the Cup-15 and other unrelated centrifuges.
Can you freely spin it by hand without the belt? Any weird sounds? Does it have the same shimmy regardless of speed?
There are many centrifuge experts on this site - probably who could come and help you out for the right price.
You sure you have the right belt? Belt have different properties as well. A bit too big or small, wrong material, etc. - can lead to issues.
Everything else is balanced? No other weird noises when it spins up? Just the vibration?
Were you able to check the torque on the bolts? Check the tension on the belt? Is it what it says it should be?