The problem is explicitly due to the way that the plugin works. it's publishing from the server time and the front page of the site is looking at the offset time. Why are you linking me to a completely unrelated post that I made years ago?
this is related to your plugin, and this issue is not yet resolved.
For a recap, your plugin is publishing posts too early, it's simply not looking at the post time offset. to be specific, I'm referring to the "timezone" settings on http://www.example.com/wp-admin/options-general.php
Here's a case example. it's 7am here, and I have the wordpress set to -4 UST. Your plugin does not respect this timezone setting and publishes posts that should not be up for another 4 hours, publishing everything that's scheduled until 11am. If I happen to write a post 'live', it shows up after all the posts that were incorrectly published by the plugin. this isn't for one or two "missed" posts, but for every single post that's scheduled.
I'm pretty sure that this is because the plugin is just looking at the post status, then looking at the server time and publishing it, without considering the timezone situation.
to be completely clear, it is THIS plugin that's causing the situation and no other. I've tested it on completely new blogs and get the same results.
please do not mark this topic resolved until it's actually been resolved.