Because that plugin is loading the events over AJAX, it may not be able to check for the current member when loading that content and so to PMPro it will look like a non-member.
It could be do to some caching that the events/slider plugin (or a separate cahing plugin) is doing as well. (If the page is cached when a member is looking at it, it won't have those messages. If it's cached when a non-member is looking, it will.)
We changed the CSS around those messages, but the logic for showing them should be the same. I'm guessing that with older versions of PMPro, the "requires a membership" message still showed up, but it just wasn't as bright and noticeable.
I hope this gives you some ideas of what to look into. Let me know if you have a more specific problem. If you sign up for support, I can try to quickly look into this for you on the site itself:
Nice looking site, btw.