Question

How these application allow users to upload their own templates? How is this possible?

Do they have some kind of a their own template engine or..?

Answer 1

Tumblr gives you two options to include your own theme:

1. If it is just for personal use: by changing the html of the theme. If you go to your tumblr-website and click on the customize button, you can edit the html. In the header file the content of your .css must be pasted between the <style type="text/css"> </style> tags. And you can add some javascript there. For the html I suggest to read the manual that Mirko Adari suggested: Tumblr Theme manual
2. If you want it to be a theme on itself: submit your theme to the Theme Garden: Tumblr Theme Garden

Blogger is a bit more rigid. Also there you can change your html file. Keep in mind that it’s markup for posts is different then Tumblr. Also custom CSS files can be added (more information on that). If you are less familiar with css and html Blogger offers some buttons so that you can change the basics to your own needs. Blogger also offers a way to backup and restore your theme. A more detailed explanation can be found here. This template file must be an .xml file. More information on the markup of this xml-template can be found here.