This is a very heavy use of metaphor, describing something by saying it is something that it isn't, or does something that it doesn't, but which creates the right impression. Thus, it is not saying that memory bombs minds - which would be essentially meaningless if taken literally.
Here, the water is "carpet bombing still, tea-coloured puddles", which is metaphor in itself, but suggests that the water is coming down quickly, in large quantities, and either creating the puddles or hitting pre-existing puddles. It's strange that there should be a "reluctant old well", itself an instance of pathetic fallacy (attributing human emotions to things that don't have such emotions, like inanimate objects), suggesting the well didn't give much water, and yet also that there were already puddles, suggesting standing water. However, the fact they are still ... puddles suggests that they existed before - as once the rain is hitting them, they are no longer still.
So, before the rain hit there were "still, tea-coloured puddles", a "pigless pigsty", and a "reluctant old well", and the rain hitting did things to all of them. Carpet bombing, as a metaphor, suggests that each puddle was hit with a lot water by the rain. There is then a simile, describing something by likening it to something else explicitly, comparing the carpet bombing of the puddles with "memory bombing still, tea-coloured minds". Thus memory is likened to water, both bombing a still, tea-coloured thing: water bombing puddles, and memory bombing minds.
Obviously, memory bombing minds is a metaphor, so you have to work out what it means. Here we have the guidance that it means memory doing to minds what the water of the rain does to puddles. Every reader will have a different idea of exactly what that means, so I don't want to give you an answer - finding your own may give you a different one, likely one that is just as valid as mine. Just think about how memory might do to a mind what the rain is doing to the puddles.
(The fact that minds are still and tea-coloured is also metaphor, of course, and the same matter of individual interpretation applies.)