I was just going to post this as a "not resolved" topic, but just as I was about to finish writing this lengthy post, I solved the issue. Therefore, I decided to finish the post anyway and simply post the solution just in case others ever encounter this issue. So for the solution, just skip down to the last paragraph.
Here is my website: http://www.rumiati.com/
I had been using a certain customized theme ("Theme 1") up until yesterday when I decided to change the theme to a different one ("Theme 2"). I thought the theme changed with no problems; however, I later realized this was not the case!
However, when anyone else accesses my website, here's what happens... If they go to the index page, this page properly displays as it should--it shows Theme 2; however, any of the other pages (About, Pictures, etc.) or posts display Theme 1. And what makes things even more confusing is that the Theme 1 that is being displayed--although it actually is the theme I was previously using, it strangely uses older versions of my website! The easiest way to see this is by looking at the tags (just copy and paste them into notepad). So for instance, each of these three pages are displaying different versions of my website: Home/Index (displays correctly), About (displays older version of my website), Pictures (displays slightly older version of my website than 'About').
I have the "WP Super Cache" plug-in installed...FRESH OFF THE PRESS--OK, now as I was just about to finish this post, I thought it would be a good idea to play around with the WP Super Cache plug-in I just mentioned above--sure enough, this was the issue! I recently enabled "Mobile device support," and now when I disabled that, the website thankfully displays the way it's meant to--for everyone!