Since there are streamers and viewers from all over the world and therefore different timezones and googling said timezones becomes quite exhausting, why not introduce a "twitch-time(zone)".Have a clock ticking (and the date) in the corner or somewhere visible. This would for sure prevent any confusion with the starts of events or streams.
Someone is streaming and announcing in the title of the stream when they are going to switch to a different game in "twitch-time"? Just take a look in the corner and you're sure to not miss it. Which timezone becomes the official "twitch-timezone", doesnt really matter.