Publication dates on posts aren’t displaying properly

I’ve noticed that this theme treats publication dates on posts really oddly.

1. If I finish drafting a post and schedule it to be published, the publication date shows up as the date I finished the draft. Eg: I finish a post on February 16 and save my progress. I schedule the post to go live on February 18. But when the post goes live on the 18th, the date of the post shows up as the 16th. If i update and republish it on the 20th, the date then shows up as the 20th.
2. Post dates in my monthly archives don’t match up with the appropriate months. EG: If I visit the archive page for August 2015, it shows me many more posts than the ones that were published that month. For some reason, the vast majority of my archive posts show a publication date in June 2016. The URLS for the affected posts still show the correct month of publication (eg: August 2015 instead of June 2016)

Can you help? I’ve checked that my settings use the correct local time zone, so it’s not that. Plus, the issue disappears when I switch to a different theme

I’ve currently put the site into maintenance mode so these issues are not visible to the public.

The page I need help with: [log in to see the link]