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Tim said today. He didn't say when today. Look for the normal times, 10:00 a.m. Pacific, 12:00 p.m. 1:00 p.m. Eastern for U.S. time zones.

Could be sooner. We will see.
 
They only mentioned iOS 12.1. Nothing about watchOS 5.1
No but MR article speculates:
"iOS 12.1 should be released alongside new updates for tvOS, watchOS, and macOS right around 10:00 a.m. Pacific Time, Apple's typical release time for new software updates."
 
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