When we create a Spawtz installation for you, we will also skin the Spawtz site to match your existing website so the Spawtz side looks exactly like your site. We do that by "ripping" the html from your site and using it in a template on the Spawtz site.
All the resource files for the skin are simply referenced from your main site - ie, all the images, javascript files and css script files are not hosted on the Spawtz site, we just link to those files on your site.
For images and css files this works fine. But in some instances, some javascript files will make requests for resources on your site "on the fly" - ie, when the page is loaded into the client's browser. Sometimes, this can cause issues with the display of the page, most usually with the display of fonts (many modern sites use javascript to "rewrite" the fonts in a page to match some better fonts than are available by default in the browser).
If you find that fonts are not being displayed correctly on the Spawtz side, it may be that you need to allow cross-origin resource sharing (CORS) on your site.
How you do this varies from server to server. An excellent site which tells you exactly how to enable CORS on your server can be found here:
http://enable-cors.org/
If you do not know how to complete the instructions listed in this site, you should be able to raise a ticket with your hosting provider asking them to complete the steps for you.