Changes to sidebars not showing on live site

I have this site up and running: (it's part of my multisite). I needed to set certain sidebars to show up on certain pages only so I added Custom Sidebars Pro.

After creating all my custom sidebars, I seem to have a caching issue. No updates to my site show immediately (sometimes they do show up hours later), and my custom sidebars don't show on the pages I've chosen.

I tried deactivating all of my plugins to see if there is a conflict but I couldn't isolate one, nor could I ever get the sidebars working.

Here's a screencast showing the problems I'm having:

Can someone help me solve this caching issue and get the Custom Sidebars working?

Thanks so much!