Fallout First Purchase Timing

Going to buy a month of 1st, and want to time it around the free monthly item.

According to the Atomic Shop, the free item for March (alien stasis chamber) resets on April 5. Then the April item will reset on May 3.

So if I buy Fallout 1st on April 4, I should get the free items for March, April and May - correct?

And follow-up question - do you get the free monthly item immediately on purchase of 1st, or does it take time to kick in? (Not worried about the atoms coming later)