re: What's the rule for pouring concrete when there is a chance of rain?

Unless it's still raining. If you run out of time, the concrete will set before you can finish it.

From a structural standpoint there's nothing wrong with placing (you don't "pour" concrete, you place it) concrete in the rain. This is true if you don't care what the finished surface will look like.

If it rains onto plastic (unhardened) concrete, the rain action washes out the mortar paste on the top of the surface leaving exposed aggregate as the surface. This is not the right way to do an exposed aggregate surface and generally the gravel used in generic residential patio concrete is different than what would be used in the exposed aggregate concrete. Different as in not aesthetically uniform or attractive when exposed to view.

Summary: Don't knowingly place patio or sidewalk or driveway concrete when there's a high rain probability.