The logo/image itself is not centered. You have extra transparent space on the right side of your logo, so even if it did center it will always appear as if it’s showing up towards the left. So first remove the extra space on the sides using Photoshop or however you created the image, and make sure its perfectly centered.
Next, to add the code to make it center on mobile devices, you can add the following to the appropriate responsive section (near the bottom of your css) –
.header-image .site-title a {
background-size: contain !important;
}
You can add it to the iPhone, or the tablet sections (they’re labeled)