What would happen if an asteroid were instantly transported to a tropical rain forest during the rainy season?

Actually, all l tropical rainforests have a rainy season and a dry season. That's in chapter one of Ecology 101. The asker also specified that the asteroid didn't "hit" the earth (in which case it would heat up in the atmosphere) but was transported instantly, as if by magic.

I also don't think the asker is expecting anyone to do calculations. Instead, this looks like one of those questions where someone asks what would happen if you drilled a hole through a earth then dropped a stone into the hole, would it come out the other side? That's a perfectly good physics question that people answer without calculations, but by thinking of things the asker may have forgotten (such as air friction).

In this case, I can think of one thing: such an asteroid would so heavy that it might sink through the crust and mantle, all the way down to the core. I don't know it if would, but it sounds like a possibility.

FFFFFFF is completely correct.

Sad to say your question is wrong. One of the things about tropical rainforests is they are rainy all year round, and at some point pretty much every day. THEY DON'T HAVE A RAINY SEASON.

Never mind calculating your puddles and your lakes - try and understand a little bit about the world you live on first.