What is Cut-Off Current in BJT transistors?
when there's 20 volts across collector and base there's no current flow, but when the voltage increases to 30
  


No. You are reading too much into the numbers. You are treating the numbers as a curve or trend, which they are not. Nowhere does it say no current flows at 20V. 


  
    some cut-off happens
  


Also, this sentence doesn't make sense. "Some cutoff happens" doesn't mean anything. It's like saying "some fast happens" for a car. Maybe you meant to say "some cutoff current flows"?

That is simply one measurement taken under the specified conditions. 

Forget the fact it even says cutoff for a second. It does not change the meaning or interpretation of  the measurement at all. The cutoff label just tells you this is intended to give you an idea of leakage currents when the BJT is off (in cutoff), but doesn't change what the measurement is saying.

i.e. Disconnect the emitter so Ie = 0, apply 30V between C and B and you get 1uA flowing through C and B. In other words, wire the BJT as just a reverse-biased diode using the collector and base junction and measure the leakage at 30V. Nothing more and nothing less. Maybe that's what you were missing? The emitter was disconnected. That's the only way they can 100% make sure Ie = 0. So the leakage current measured must be between B and C.