There is a rather disturbing contradiction in the seed note.
First it says
"Back up your Mac.
Always back up your data and files before installing beta versions of macOS. If you have multiple Mac computers, we strongly recommend installing on a secondary system. Backing up files on a Mac is easy with Time Machine, the built-in backup utility."
Then later in the seed note it says
"Time Machine is disabled for macOS High Sierra 10.13 beta 2 update 1 (17A291m). Apple recommends turning off Time Machine for APFS volumes on earlier versions of macOS 10.13 beta 2 as the space for snapshot files may not be freed correctly."
And that build 17A291m is the same as the public beta. So this explains why time machine isn't working in the public beta.
I think they should have fixed it before releasing the public beta - even if it meant not meeting the deadline of "end of June".
I hope they will fix it before releasing the golden master. They should not release a broken system.