SD cards already have a processor inside them to handle the SD protocol and to talk to the actual raw flash chip inside. The Eye-Fi card has a processor that is capable of doing WiFi and a tiny WiFi transceiver + antenna as well. All of this stuff has been miniaturised already for other purposes so putting it all into a big SD card package isn't that difficult.

Micro-SD cards use the same sort of controllers and they're pretty powerful controllers at that. The difference for Micro-SD is that the controller isn't packaged up first. Its just a bare silicon die that gets put into the card.

You can see the insides of an old Eye-Fi card here.