All old test results, from the day before, are first removed before the new test results are stored.
This means, whenever you login into Adalysis everyday, what you will see are the updated test results based on your Ads performance data up to yesterday.
All dates and times are relative to the adwords account's own timezone. Every adwords account has a timezone associated with it and Adalysis works out the time for the daily refresh and test run based on that timezone. If you have an MCC with few adwords accounts, it's important to remember that these accounts might have different timezones and, if that's the case, your adwords accounts test data will be updated at different times during the day.