The plugin wasn’t designed to work like that.
It can add the classes for the Font Awesome webfont set if you use a plugin or theme that includes the font awesome files or another icon font set that makes use of equivalent classes.
Other webfont sets are not directly supported, but can probably be made to work by using the same classes as used by Font Awesome in the stylesheet.
As an example, if you give the icon parameter the value “cog” in the shortcode
[tabby title="My Tab" icon="cog"]
This will add the classes fa & “fa-cog to the tab’s title. If you have a theme or plugin that adds Font Awesome icon font files and stylesheet to your site, the icon will then appear in the tab title.
If you want to continue using the icon plugin you mentioned, the css you need to add to your child theme will need to include rules some for the fa class:
.fa {
display: inline-block;
font-family: wp-svg-plugin-icon-set1;
font-style: normal;
font-weight: normal;
line-height: 1;
font-size: 0.8em;
-webkit-font-smoothing: antialiased;
-moz-osx-font-smoothing: grayscale;
}
Plus a single rule for each icon you want to use. For the cog icon the rule would look like this:
.fa-cog:before {
content: "\e08e";
}
The optional Tabby Responsive Tabs Customiser add-on plugin can add the Font Awesome files for use with Tabby Responsive Tabs (and elsewhere on the site) and can be used without requiring any editing of theme files.