There is no 'auto play' for the main slider and 3 child sliders by default. It is controlled by manual API call.
By removing following code, you will get what you want.
function OnMainSliderPark(currentIndex, fromIndex) {
$.each(nestedSliders, function (index, nestedSlider) {
nestedSlider.$Pause();
});
setTimeout(function () {
nestedSliders[currentIndex].$Play();
}, 2000);
}
jssor_slider1.$On($JssorSlider$.$EVT_PARK, OnMainSliderPark);
OnMainSliderPark(0, 0);
Also, the grid slider is a variation of nested slider.