We have a azure web application where in there is one search box, when we enter text with double quotes like \"App Service\" it correctly list records with \"App service\" h
In Azure Search we use Lucene's Postings Highlighter. This highlighter ignores positions of terms that matched, that's why you see all phrase terms highlighted independently. Unfortunately there is no way to customize this behavior at the moment. I realize this could be confusing to your users.
Please use our UserVoice page to vote for changing the current behavior.