Mostly probably not so soon, because, to be a big fragment, enough to cause large damage to Motavia could not have a high speed (considering spatial speeds and distances)
Considering the forces involving a satellite crash with a planet, the planet would never have exploded. Even if Mars crash on Earth, Earth will not explode. Part of both planets will be scattered in the space, but Mars core will blend with Earth core, forming one new planet.
What I consider is that the crash of Gaira with Palma was so strong that it crumpled the part of the planet where the crash happened, but it didn't destroy the planet at once. It is like a huge asteroid hit the Earth and the mankind would eventually be extinct, but not at once. That is why I think Palmians were able to build some large spaceships and flee the collapsing planet. Palma would not have exploded, but would have turned into an uninhabitable mass.
In PSII, Gaira doesn't look much larger than a spatial station. As a result, it couldn't be traveling at near light speed, otherwise it would pass through Palma, causing less damage than a regular collision, because it would not lose all the energy. It would also not generate debris enough to cause damage to Motavia. Being so, the theory of a non-explosive collapse in Palma seems more likely, with Gaira being big and fast as a large asteroid.
The debris from the collision between Palma and Gaira could not travel so fast, otherwise that meant almost no energy was spent in the collision. In fact they would be much slower than Gaira. Considering a regular distance between the planets (over 10 million miles), it would take months, if not years, to a large fragment of Palma, enough to cause the "Great Collapse", hit Motavia.
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