Why is alchemy powered by tectonic plates?
Seriously, the most explanation we ever get is this one panel in chapter 67:


If you're wondering how this manages to do transmutations other than earth based ones, remember, the earth isn't the source of the transmutation itself, just the energy used in it. Just the necessary materials (the equivalent exchange) aren't enough to perform a transmutation. You also need the knowlede of how to rearrange the material to its new form (which is why alchemy isn't more widely used) and the energy to actually do the rearranging.

Amestris' alchemy uses the energy in the ground (previously caused by plate tectonics, currently by... Well, let's not spoil it), while earter alkahestry uses natural chi flows.

How?
Never explaned beyond that one panel, since it's not really important to the story.
Cool action and existential philosophy are.