Amazon normally releases content on the day advertised as 00:00 GMT, which for US shows is the day before at 8pm ET. But I do see "Coming soon – June 13, 3:00 AM ET" on the season 4 page (archived version). The air dates have been updated.

Even if Amazon released the show the day before at 8 eastern, why is it any different than Doctor Who? That one gets released at 8pm eastern the day before it come out, why is it then set to the advertised date? Also, this ambiguity would be solved by having a release time property for episodes, is that something that’s been considered?

@bradr3d said:

Even if Amazon released the show the day before at 8 eastern, why is it any different than Doctor Who? That one gets released at 8pm eastern the day before it come out, why is it then set to the advertised date?

Because Doctor Who is a British show that airs Saturday nights on BBC One. Since Doctor Who is a UK-produced show that airs on linear TV in the UK, its release time outside of the UK is irrelevant.

Also, this ambiguity would be solved by having a release time property for episodes, is that something that’s been considered?

Yes, you can vote for it on TMDB's Trello: https://trello.com/c/eZ2o4jmD/229-add-released-time-to-episode-air-dates