The day-long window for each collection will cover all time zones, so as long as you visit the collection on the correct day, you should be able to search and view that day's free records to your heart’s content.
I'm not going to list all of the included collections in this post (you'll find them on MyHeritage's blogpost here if you want on to check them out).
Instead, I'm noting below only those I consider of most relevance to family historians with Irish connections. The exclusive collections are in bold type.
Since the promotion started on Monday, the free collections have been Scandinavian records. But starting from tomorrow, we have:
Friday 5 June: U.S. City Directories United States
Saturday 6 June: U.S. Social Security Applications and Claims, 1936-2007
Sunday 7 June: Chronicling America: Historic American Newspapers, 1836-1922
Monday 8 June: Ellis Island and Other New York Passenger Lists, 1820-1957
Tuesday 9 June: 1940 United States Federal Census United States
Wednesday 10 June: Massachusetts Newspapers, 1704-1974
Thursday 11 June: Historical Books: Index of Authors/People Mentioned, 1811-2003
Friday 12 June: Compilation of Published Sources
Saturday 13 June: Canada Newspapers, 1752-2007
Sunday 14 June: 1921 Canada Census
Sunday 21 June: England & Wales, Death Index, 1837-2005
Sunday 21 June: England & Wales, Marriage Index, 1837-2005
Monday 22 June: 1939 Register of England & Wales
Wednesday 24 June: Australia Electoral Rolls, 1893-1949
Access to these collections on the specified days will be completely free, but free registration to MyHeritage (it's a quick and simple process) will be required for non-MyHeritage users.
NOTE: I got my days of the week muddled when I first published this post. I've now corrected them. Apologies for any confusion caused.