OK, es war das transition-delay dass gefehlt hatte

transition-delay:2s;
animation-delay:2s;

nun geht es super mit:

.avia_transform .av_slideshow_full .avia-caption-content, .avia_transform .av_slideshow_full .avia-caption-title,
.avia_transform .av_fullscreen .avia-caption-content, .avia_transform .av_fullscreen .avia-caption-title, 
.avia_transform .av_fullscreen .avia-slideshow-button, .avia_transform .av_slideshow_full .avia-slideshow-button
{
-webkit-transform:translate(0,0);
transform:translate(0,0);
visibility: hidden;

}

.avia_transform .av_slideshow_full.avia-fade-slider .active-slide .avia-caption-content,
.avia_transform .av_fullscreen.avia-fade-slider .active-slide .avia-caption-content
{
visibility: visible;
-webkit-animation: caption-bottom 2.5s 1 ease-out;
animation:         caption-bottom 2.5s 1 ease-out;
transition-delay:2s;
animation-delay:2s;
}

.avia_transform .av_slideshow_full.avia-fade-slider .active-slide .avia-caption-title,
.avia_transform .av_fullscreen.avia-fade-slider .active-slide .avia-caption-title
{
visibility: visible;
-webkit-animation: caption-top    1.5s 1 ease-out;
animation:         caption-top    1.5s 1 ease-out;
transition-delay:2s;
animation-delay:2s;
}

.avia_transform .av_slideshow_full.avia-fade-slider .active-slide .avia-slideshow-button,
.avia_transform .av_fullscreen.avia-fade-slider .active-slide .avia-slideshow-button
{
visibility: visible;
-webkit-animation: caption-top  1.2s 1 ease-out;
animation:         caption-top  1.2s 1 ease-out;
transition-delay:2s;
animation-delay:2s;
}