Do players get a free Prismana at launch?

The reward is a choice, not a random hand-out. You pick which rare Prismana you walk away with, so it is worth slowing down on that screen instead of tapping through it. A rare unit you select deliberately is one you never have to chase.

Reaching the rank of Junior Wayfarer, which also appears as Junior Excursionist, grants a choice of a free Prismana Aniimo as well. The Prismana you get for free are front-loaded into the opening hours of the game rather than spread across your account's life, which matters for how you plan a starting team.

The Prismana is not the only thing waiting at global launch. Eggs are part of the same package, including a free Perfect Egg. Between the two you start with a rare Aniimo of your choosing and hatchable stock, so there is no early stretch where you are working with nothing.

Getting Prismana after the free one

Two routes matter once the launch rewards are spent. Landing a Lucky Strike while catching an Aniimo has a chance to trigger Prismana flow on the spot, which makes catching worth doing carefully rather than spamming attempts.

The other route is nurturing. The base chance of a Prismana Aniimo appearing there is flat and stays the same on every attempt. It does not climb as you keep trying, so a long run of nothing leaves your odds exactly where they were on the first go. Budget your attempts on that basis, not on the assumption that you are due one.

Not settled: Whether the launch reward and the Junior Wayfarer grant are two separate Prismana or the same pick delivered at that rank is not settled.