This is the number one question and the answer is simple: validity starts when the profile first connects to a network in the country the plan was bought for. Installing spends no days at all.
Why that matters
It means you can install a week before you travel, on your own Wi-Fi, and lose nothing. We recommend exactly that, because installing needs internet.
How not to activate it early
After installing, leave data switched off for that profile. The profile sitting in your phone does nothing until you let it connect.
On iPhone: Settings > Cellular > select the eSIM line > turn off Turn On This Line, or leave the line on with data off.
On Android: in the SIM manager, switch that line off until you need it.
What counts as a day
A day is twenty four hours from activation, not a calendar day. If the profile activates at six in the evening, a seven day plan runs until six in the evening on day seven.
If the plan expires with data left
Unused data does not carry over into a new plan. So pick a validity that matches the trip rather than the longest one available.