To set up your own mail notification, simply make a new AppleScript in Script Editor, and paste my code into the new script. Replace this line:
<<Your Phone's e-mail address>>
...with your phone's e-mail address (see this page to find out what your address is, or Google it). Save the script wherever you'd like.
Now, in Mail, make a new rule (Preferences: Rules: Add Rule), or just modify an existing one. Set whatever "If" criteria you want, then under "Perform the Following Actions," select "Run Applescript" then choose the script you just made. Make sure the rule is active, and you're done!
Now, due to some weird bug with AppleScripts in rules, when I tested this at first, it seemed like Mail was not applying the rule to test e-mails I sent to myself. However, since then, this script has performed flawlessly in notifying me promptly whenever I receive new mail from select contacts.

