"Read more" is displayed even when the text is shorter than excerpt size

If I understand you well, you would prefer “read more” to be omitted when a post is so short, that there is really nothing more to be read! But, this is the way WordPress works. Even if a post is only a few words long, so that its full contents are ‘exhausted’ in the index page, a link still exists to a single page devoted to that post.

Auto Limit Posts does the same, it offers in all cases a link to the single post page, even if everything is already said in the index page. Usually a post is longer than a few words, so that Read more normally can be considered a proper invitation, however, if your posts are usually tiny, you can change Read more to, e.g., “Post Page”, “Permanent Link”, or whatever you may think would be a better alternative!

Thank you! Good advice, I will follow it! But, personally I would prefer though that the “Read more” to not appear at all for tiny posts.