Google Fonts Do Not Work With Gmail Or Outlook
Webfonts do not work in all email clients. They do not work with Gmail, Yahoo, Android clients and spotty support for Outlook 2007-2016. I know this sounds ridiculous, since Google has Google Fonts, but the current reality is that Gmail does not support Google Fonts.
You need to settle on a fallback font which is not Tillana or Open Sans, which is also a Google Font. In your case, the backup font for Gmail will be Arial.