There are a few reasons your older website is still appearing when you visit it in your web browser.
1. You just switched to EverWeb Hosting and didn't update your nameservers.
This is a very common issue. Nameservers tell a domain which server to point to and must be updated (they can take up to 72 hours to fully update). You can learn more about changing your nameservers here.
2. You're visiting an older URL in your web browser.
At the very top of your web browser in the path field, you will see your website URL or address. You may have visited an older URL that is still stored in your web browser and is being autofilled. Make sure that when you visit your website you are just visiting your domain name (ex: http://www.yourdomain.com).
3. You are visiting a cached version of your website
When you visit your website your web browser may store some website resources locally on your computer so the next time you visit your site it loads faster. That means other people are not seeing what you see because they don't have these stored files yet. This is called website cache and it is usually deleted automatically after a few minutes.
The easiest way to check if this is the case is to turn on private browsing in your browser and visit your website. Then you will see your site how everyone else will see your website.
4. Quit your web browser and reload your website.
Sometimes you just need to quit your web browser and reload your website to see your changes