What is happening from your description is that your small 32 x 32 images are being made bigger on your mobile device with its small screen.
This may be that your device is using a version 4.x html where width & height could be selected as either % or px as controlled by the application. With html v5 the definition is fixed in px. So that would explain why you are seeing a much increased size. The max-width setting avoids that problem.
Could you check which version of html your troublesome device is using please.
I am not familiar with the code in the 1.9.2.x series but you would probably find the code in somewhere like <site>/components/jdownloads/views/download/tmpl/default.php (that is structure used in the 2.5 and 3.2 series. The 2.5 and 3.2 series are just about to go stable so you might like to think about upgrading on a test site. If you find the problem there then we can definitely fix it!!