Videos on iPhone say "download file"

I had previously had a plugin for displaying videos that wasn’t cross-browser compliant. So I upgraded to WP 3.8 and deleted the plugin and am now using the standard core shortcode for videos. They seem to work fine on Firefox and Chrome and IE but for Safari (at least on the iPhone), all I see is a black box with the link “download file” — which seems to load the video when clicking. I don’t want to display a box and a link like that, how can I have the video’s thumbnail with a play button displayed instead? The video is a M4V format.