Using ST3 build 3125 x64 in win10 x64.
For example (from here)
var str = "Hello, " + name + "!";
var str = `Hello, ${name}!`;
Here is how it's highlighted in ST3: (see the name variable in line 2)

And, for reference, here is in VSCode 1.5.3, i.e. correctly:

And another example:
let arr = [], temp;
$.each(arr, (index, value) => {
arr[index].innerHTML = '(' + temp + ') ' + arr[index].innerHTML;
arr[index].innerHTML = `(${temp} ) ${arr[index].innerHTML}`;
});
In ST3: (see both temp and arr[index].innerHTML in line 5)

and for reference, here is in VSCode:

Related issue: #213
This is more to do with your color scheme than Sublime itself.
Mine is showing as:

with the declarations:
<dict>
<key>name</key>
<string>JS Template Expression Definition</string>
<key>scope</key>
<string>string.template.js punctuation.definition.template-expression</string>
<key>settings</key>
<dict>
<key>foreground</key>
<string>#515151</string>
</dict>
</dict>
<dict>
<key>name</key>
<string>JS Template Embedded Expression</string>
<key>scope</key>
<string>string.template.js source.js.embedded.expression</string>
<key>settings</key>
<dict>
<key>foreground</key>
<string>#d3d0c8</string>
</dict>
</dict>
I'm using the Monokai scheme (=the default one) which is in its initial status (I haven't modified it at all),
Iirc @wbond wanted to clear the string scope name (using clear_scopes) for embedded expressions like these.
related discussion: https://github.com/sublimehq/Packages/issues/715
Most helpful comment
Iirc @wbond wanted to clear the string scope name (using
clear_scopes) for embedded expressions like these.