There is no need to save the home location with the time.
If you save the UTC date of the event, the localized date for some timezone can be extrapolated from it.
If you save the UTC date of the event, the localized date for some timezone can be extrapolated from it.
I just wanted to highlight that "time" is a human concept that in informal setting means a lot of things, but when you start to model it formally, it can be more complex than a single timestamp.