Fonts display incorrectly in Google Sites but only when publishing to custom domain

We've done a simple Google Sites and changed some fonts to Montserrat and Helvetica Neue. These fonts display perfectly on the sites.google.com/view/mysite page, as you can see below:

However, when using a (previously set up) custom domain to access the website, all 'manually changed' fonts default to either Arial, Courier New, Georgia, Roboto, Times New Roman, Trebuchet MS, Verdana or Times New Roman (mainly Times New Roman). I don't have a clue why. HTML code is the same between both websites so we don't know what's going on. If someone is able to guide us a bit, it´d be very appreciated