My changes in Theme Options are not being applied to some pages/posts, why?

There could be two main reasons for this:

Caching Plugins

Please check if you (or your hosting company) are using any caching plugins such as WP Super Cache, W3 Total Cache, LiteSpeed Cache, etc. If this is the case, you need to empty the caches of these plugins before visiting the frontend of your website to see the changes. Caching plugins save the pages of your website in static cached files to speed up the loading time of web pages. Until these cached files are not cleared, no changes will be visible on the frontend.

Three-Tier Hierarchy

In TheGem, Theme Options are built reflecting the flexible three-tier template hierarchy approach:

Tier 1: Theme Options allow you to make global website setup, which will be automatically applied to all single pages & posts and all archive pages (see “Global Website Settings”) .

Tier 2: Additionally, you can make separate settings for chosen types of single and archive pages (posttypes) , which will differ from global settings and will apply only on this selected types. For example, if you wish, that all your blog posts or product categories have different layout & styles than the rest of your website, you can easily make this custom settings in Theme Options (see “Single & Archive Pages”).

Tier 3: And finally, using Page Options, you can setup individual pages, posts, products etc. to look differently than set for the whole website (Tier 1) or for the selected post types (Tier 2).

Simply put:

The custom settings made for some specific post in page options

override the custom settings made for the all posts in Theme Options -> Single Pages -> Post

And the settings made in Theme Options -> Single Pages -> Post (see screenshot above) override the global website settings made in Theme Options in "General", "Menu & Header", "Title Area" and "Footer" sections

So, in case some of your settings made in Theme Options are not reflected on some pages/posts/products etc. just check, that there are no custom settings set in "Theme Options -> Single Pages" (or "Theme Options -> Archive Pages") which override the global settings you have made AND there are no custom settings set in page options of the certain page/post which also override the settings made in Theme Options.