I'm nearly certain that it's your theme or another plugin that is interfering. Here's the deal; If you look at the HTML source of a TubePress thumbnail image, it should look something like this:
<div class="tubepress-thumb js-tubepress-thumb js-tubepress-fluid-thumb-adjustable">
<a class="tubepress-cursor-pointer js-tubepress-invoker js-tubepress-itemid-1QOe4k-LaSY">
<img class="tubepress-thumbnail-image js-tubepress-fluid-thumb-reference js-tubepress-preview" alt="New Year's Eve wedding film {Tulsa, Oklahoma wedding video}" src="//i.ytimg.com/vi/1QOe4k-LaSY/mqdefault.jpg" width="167" height="94"/>
</a>
...
but on your site, it looks like this:
<div class="tubepress-thumb js-tubepress-thumb js-tubepress-fluid-thumb-adjustable">
<p>
<a class="tubepress-cursor-pointer js-tubepress-invoker js-tubepress-itemid-nYVDLjEnJhY">
<img class="tubepress-thumbnail-image js-tubepress-fluid-thumb-reference js-tubepress-preview"
<br />
alt=”NuCanoe Frontier vs Amberjack by Graham Tayloe” src=”http://i.ytimg.com/vi/nYVDLjEnJhY/default.jpg”
<br />
width=”160″ height=”120″ />
</a>
</p>
...
Notice the extra <p> and <br/> tags? Usually that's causes by a WordPress filter (from a theme or plugin) messing with the HTML output before it hits the screen. It looks terrible, of course, and breaks TubePress's client-side functionality. To find the offender, first I'd switch your theme (or even just preview) to WordPress's twentyfifteen or something extremely simple. If the problem persists, you know it's a plugin. I'd disable your plugins one by one until the problem goes away. Tedious, yes, but it's an effective way of narrowing down the cause.
Thoughts?