When Vadic first addresses the Titan's bridge personnel, she says, "Good afternoon. I believe it is afternoon in the Sol System."
Afternoon is a relative term, based on where on a rotating planetary body an observer is. On any planetary body, it is afternoon on 1/4 of its surface. Also, the Sol System has several planetary bodies (regular and dwarf planets), which each have their own afternoon. So Vadic's reference to the Sol system's afternoon makes no sense.
However, starships *do* use times and dates, so it is possible that Federation ships all synchronize to one timezone on Earth, and that this timezone is therefore the "Sol timezone", the timezone all Sol-based starships use, and is the one Vadic is referring to.
Afternoon is a relative term, based on where on a rotating planetary body an observer is. On any planetary body, it is afternoon on 1/4 of its surface. Also, the Sol System has several planetary bodies (regular and dwarf planets), which each have their own afternoon. So Vadic's reference to the Sol system's afternoon makes no sense.
However, starships *do* use times and dates, so it is possible that Federation ships all synchronize to one timezone on Earth, and that this timezone is therefore the "Sol timezone", the timezone all Sol-based starships use, and is the one Vadic is referring to.