One thing to note with any USBasp working with the Arduino IDE, there is a limitation that the IDE is not able to select a slow clk option with the USBasp programmers. So I did have to jumper JP3 on the USBasp board to force the slow clk option to program the ATtiny13A running at 128KHz.
That is how my USBasp worked when I first got it, it would work but upon the completion of a action avrdude would print a warning message about needing a firmware updata to allow for CLK speed selection. So I found a newer firmware version on the hobby king support files folder, so I loaded the newest dated firmware file onto my USBasp and now it still works but the warning message is gone. My programmer did not have a J3 jumper for speed selection.
Lefty