Can this be added in a PHP template?

Couldn’t you just use the do_shortcode() function? It’s pretty simple to use usually.

How it’s usually used in it’s simplest form:
<?php echo do_shortcode( '[shortcode]' ) ?>

The tooltip shortcode is a little different because we also have a closing tag:
[/tooltip]

So we write the full shortcode this way:
[tooltip tip="Popup tooltip text."]some text here[/tooltip]

Ok, fine. So to do this in PHP, I would first assign a variable for the “some text here” portion so that we may neatly call this in the do_shortcode() function:
$tooltip_text = "some text here.";

I will then simply display the results of the shortcode using the echo construct:
echo do_shortcode( '[tooltip tip="This is the tooltip popup text."]' . $tooltip_text . '[/tooltip]' );

As you can see, we’re echoing (or displaying) the shortcode exactly as we would normally, only this time using a variable for the title text.

The full PHP code would look something like this. I put mine inside <div> tags:

<div class="tooltipShortcode">
<?php
$tooltip_text = "Title text of the tooltip.";
echo do_shortcode( '[tooltip tip="This is the tooltip popup text."]' . $tooltip_text . '[/tooltip]' );
?>
</div>

For more information on using shortcodes in PHP, check this out:
http://codex.wordpress.org/Function_Reference/do_shortcode

Hope this helps. Have fun!