I have tested the theme and could not reproduce the reported problem
i used this settings http://prntscr.com/w3an3v and the front page look like http://prntscr.com/w3anld – so the both header transparent and background image works as expected.
Looking over your page i see that there is no image saved as background http://prntscr.com/w3aoh3. Are you sure you saved the settings correctly ?
If yes and the problem still appears we could investigate the issue, but we will need access to your wp-admin area.