Given a fuse panel, which way should a fuse tap be facing?

If you are running an inline fuse (which you should), you put it on the power side. This is so you don't overtax the fuse you're tapping off of. To tell which is hot, pull the fuse and check each side for power. Power off of the side you get a reading.

And yes, the hot/cold should be same for the entire column ... I'd still check it if I were you though. You know what happens when you ass/u/me something, right?

EDIT: On your tap, the power is obviously provided off of the side which has the wire. From your description, the manufacturer wants that side to be on the dead side so the fuse will provide coverage for your needs. My suggestion is to get a second fuse (inline type) and put it at the wire's end. Then turn the tap around so the power is to the wire side. The reason being is, if you use the same size fuse for the original circuit and for your new circuit, you have the propensity to burn through the fuse. You could end up changing fuses on a regular basis. If you do it as I'm suggesting, you have the original circuit being provided protection from the original fuse, then you have the secondary fuse providing protection for the new circuit. Everything remains happy without issue. You DO NOT want to put a larger fuse in there to handle additional load, because the original circuit will have the ability to draw too much, which could cause other issues.