ATTINY85 pin doesn't go fully LOW when in PWM
In datasheet of this mcu is this behaviour explained and also hints at how to change it.


  If
   the OCR0A is set equal to BOTTOM, the output will be a narrow spike for each MAX+1 timer clock cycle. Setting the OCR0A equal to MAX will result in a constantly high or
   low output (depending on the
  polarity of the output se
  t by the COM0A[1:0] bits.)


Meaning that they cant reach 0% PWM, but they can reach 100%. For your aplication you can then invert outputs and invert meaning in code. 

OCR0A = 0x00; //fully on
OCR0A = 0xFF; //fully off


This will turn off LED completely.