colinfleming I can't reproduce this links issue in my basic use of the FastMail web app. So, it will be hard for me to help here.
I see that the FastMail web app uses www.fastmailusercontent.com as a Source. You might try manually adding www.fastmailusercontent.com in Orion's Compatability Mode setiings:
Orion > Preferences > Websites tab > Compatability Mode from the list > click the + icon > add www.fastmailusercontent.com
To be clear, I don't know that this will resolve your issue. I'm just looking for anything that might help.