How to get custom image size for image uploaded in Customizer

Apparently, your mod is storing the complete path to the image as a string. That leaves you little alternative but to do a search and replace on the string:

$img = get_theme_mod('image-1');
if (!empty ($img)) {
  $img = preg_replace ('.(jpg|jpeg|png|gif)$','-525x350$0');
  if (!file_exists($img)) $img = get_template_directory_uri().'/images/default.jpg';
    }
  else if (!file_exists($img)) $img = get_template_directory_uri().'/images/default.jpg';

In words. Get the mod. If it exists search $img for the occurence of jpg|jpeg|png|gif at the end of the string and then prepend it with the image size, eg ...image-525x350.jpg. If that file does not exist, use the default. If there is no mod, also use the default.