It's a problem that many have encountered; there are several open and closed issues on the repository. Issue 98, opened 1 month ago, describes it, and there is a pull request (102) addressing this. On the other hand, the maintainer has stated last year that this has already been solved. Finding out if it's a repository or documentation problem.

Built the Jekyll site in localhost using bundle exec jekyll build and found out that Jekyll was the one ignoring the CNAME file, not jekyll-action.

Solved by forcing the inclusion of CNAME file, following Jekyll configuration options.

Issue solved but, at the moment, it is not clear why some Jekyll sites must make it explicit and others not.

Built the Jekyll site in localhost using bundle exec jekyll build and found out that Jekyll was the one ignoring the CNAME file, not jekyll-action.

Solved by forcing the inclusion of CNAME file, following Jekyll configuration options.

Issue solved but, at the moment, it is not clear why some Jekyll sites must make it explicit and others not.

Thanks for that, I think that worked for me 👍

Built the Jekyll site in localhost using bundle exec jekyll build and found out that Jekyll was the one ignoring the CNAME file, not jekyll-action.

Solved by forcing the inclusion of CNAME file, following Jekyll configuration options.

Issue solved but, at the moment, it is not clear why some Jekyll sites must make it explicit and others not.

@martinmorando Also worked for me! Thanks so much, that was a frustrating issue :)