AFAIK you should only set the strobe mode knob to HSS when the camera is in HSS mode. If your A7RIV behaves in the same way as my A6700, you should see 'HSS' next to the flash lightning bolt symbol when your shutter speed exceeds normal sync speed (1/160s for me, should be 1/250s for you). The triggering signal for HSS is very different from a regular pulse. I don't have an MF-2, but with my Retra Pro, if I have the camera in HSS mode but the strobe in regular flash, it will fire out of sync, and vice versa.
Very strange; normally such a delay would be associated with a long exposure + rear curtain sync, but evidently that is not the case. Does the delay occur at the trigger or the strobe, i.e. if you look at the LEDs, do you see them flashing 2-4 seconds after you pull the shutter, or do the LEDs fire immediately and then the strobe firing is delayed? Do you have a regular land flash you could put on the hot shoe and test with?