The power supply is supposed to fit in the box with the controller and relay? Is this a homebrew creation, or a UL approved wiring device?

In any case, it sounds like you have switch loops for both of the switches (no neutral). This is a problem for installing electronic switching devices. I'm afraid you'll have to bite the bullet and fish a new loop from your receptacle with a neutral in it (14-3 or 12-3 instead of 14-2 or 12-2).

In some cases, it might actually be easier to rewire so that the controller is in the cellar below the box.

There are a number of problems here. First off, if there are 120V connections inside the box, the stuff in the box had better be rated for 120V which some hobby shop 12 relay or cheap controller may not qualify.

If this isn't a UL approved unit for switch replacement, Ron is right, the problem is isolating the low voltage and line voltage sides. The easy way to do this and meet code is to use a box mount fan relay. I'm having trouble finding an example right now, so it may be that relays alone aren't common any more. The replacement seems to be a fan control center which also includes a 24v transformer.

With these, the low voltage wiring stays outside the junction box. You would use your micro-controlled relay to pull in the fan control relay, which would then operate your receptacle. If appearance matters, you'd probably want to mount it in the cellar below the receptacle to be controlled.

Technically, to be 100% code compliant, you would make sure the fan relay you buy states in its installation instructions that it's suitable for fan control "and other uses," or similar language.