The strobe does fire when the internal flash fires. There is only one setting on the flash - "on". It was an entry level slave strobe made before digital cameras. I'm still thinking it may be a timing issue.
Like I said, you need to alter the camera settings to match the strobe or as you suspect, the strobe is not firing when it should, when the shutter is open. The A570 has both preflash and no preflash capability in several modes. If your strobe requires a preflash then you will need to set the A570 to preflash in the mode you are using. It will always preflash in Auto and Program. If your strobe does not need a preflash then you can only shoot the the A570 in Tv/Av or Manaul and go into the camera menu and set the camera strobe to manual and probably lowest power. This will cancel the preflash.
I do not believe your strobe expects a preflash. You will need to set your A570 internal strobe to manual, set power to 1/3 or 2/3 as needed to trigger the external strobe, use your A570 only in Av/Tv or Manual.
If, however, it turns out that it does expect a preflash, set the A570 to Auto or Program modes or set the camera to Av or Tv and set the camera strobe to Auto under the Menu button. I don't think you can use the camera Manual exposure setting since this mode never preflashes as I understand it.
To repeat, the strobe manual/auto choice is under the Menu button, the manual strobe power level is under the Func Set button.
If this does not help, well, hope somebody else steps up for you or just buy a better strobe I guess. Good luck, it would be nice if it would work for you.
N