All the syntax highlighting is provided by Textmate syntax definitions, and thus not directly controlled by Sublime Text. Several of the definitions, among those PHP, are a bit out of date and should be updated at some point.
I have updated myself and get reasonable heredoc highlighting, like this:
As you can see, the css highlighting is wrong in both cases.
Anyways, if you want to try updating you can find the latest Textmate syntax here: github.com/textmate/php.tmbundl ... r/Syntaxes
Also note that the syntax indicator in the lower right will not change if the embedded syntax changes.