Well I had no luck figuring out what is going on. The php code generates this:
<th class='easySpoilerTitleB' style='text-align:right;vertical-align:middle;font-size:100%; white-space:nowrap;'>
which puts the button on the right for you. For some reason your page has this:
<th class='easySpoilerTitleB'>
This is actually impossible. There is no php code that can generate just that line. Without that extra logic the button will be as you see it (the text-align:right is actually the important bit for this).
If you don't mind I would ask that you do three quick things?
1. Check from your admin page that you don't see two easy spoilers (i.e. if perhaps you had made a backup copy of the older spoiler plugin and by accident have two spoiler php plugins competing).
2. Can you email me the easy-spoiler.php you have?
3. Can you delete your caches (i.e. supercache or whatever you use) that would cause the spoiler php code to regenerate the page? You can also edit the page and just insert and delete a space to cause the "update" button to be clickable and the new page will be made.
That .js update you grabbed from the forum a while back is not involved, btw. This is just with the easy-spoiler.php file.
ps even tried your theme but works fine....

-d