$(document).on(':typedcomplete'
The section of your example that starts with the above is JavaScript code, which needs to be wrapped within a <<script>> macro if you want it to execute within the current Passage. You also can't embed TwineScript code within that JavaScript code the way you are doing it.
The following shows one possible way to achieve the effect you are looking for, it uses a display: none style to hide the div element containing the links, and then uses a jQuery show() function to reveal it again. I also replaced the jQuery on() function with the one() function because you only want that event handler to activate a single time in the use-case.
<<nobr>>
<div class='container'>
<div class='topBackground'>
<div class="typed-speed80-delay800">here's some text hopefully it's in the right place</div>
</div>
</div>
<div id="links" class='textBubble' style='display: none'>
[[it's a link that's really really really really long because i to test the css formatting]]
</div>
<</nobr>>
<<script>>
$(document).one(':typedcomplete', function () {
$('#links').show();
});
<</script>>
note: I have added extra line-breaks into the above just to make it a little more easy to see the different sections, those line-breaks can safely be removed.