Initialize TimeZone during DefaultClockProvider init

This is a duplication of Ie8b08bec36bccfda5a1f1eb20c91a040c1f688ab
for the refactored clock code. It's validated via unit test as it
has proved somewhat tricky to reproduce manually.

Test: atest DefaultClockProviderTest
Fixes: 241729527
Change-Id: I0c664750190572790e71f6095a1ac8c4995c83ca
(cherry picked from commit c6bfa32a)