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.
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:
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.