Hi,

1/ When you write a posts and publish it first time - that's published date.

When you go to edit that post after that and update the posts - that's modified date.

So, you can understand how that option works.

And of course it can't be auto display the year as you want. You need to edit your posts > click on "Update" button to get the date updated.

2/ If you check on Customize > General Options > "Display Modified Date Replace with Published Date" - All your posts will display modified date by default.

But:

a) It can be update late on Google because it based on how long your posts re-index on google.

b) It can be modified by a SEO plugin you're using. So, maybe you should check with seo setitngs from seo plugin you're using. It's issues from your-end with the config - doesn't related with the theme itself.

Best Regards,

PenciDesign