Custom site template not showing up in list when creating new site

I upgraded a site collection from 2010 to 2013.

There is a site template called "My Site Template" which shows up in solution gallery (in Site Settings) in both 2010 and 2013. I can also activate and deactivate it in 2013.

I have also deactivated and reactivated same site collection features in 2013 that are in 2010.

This template is showing up in "Custom" tab when you try to create a new site in 2010. But the same template is not showing up in "Custom" tab in 2013 (when creating new site)

In fact "Custom" tab is not even there in 2013.

I also have a code where I am reading that template. When looping, I can see that template in 2010 but same template is not coming up in 2013.

SPWebTemplateCollection templates = site.GetWebTemplates(1033);
foreach (SPWebTemplate template in templates)
{
}

I am stuck in this issue for the past 2 days and read many solutions but none are working.

Here's another person facing same issue but no luck.

http://sharepoint.stackexchange.com/questions/98722/custom-site-template-uploaded-and-activated-in-site-solution-gallery-are-not-com

How do I make that template appear?