Whilst I agree that you cut on the down stroke (I presume that equates to Frank's pull stroke), the teeth should always face in the direction of the line of cut. Most coping saw blades can be rotated through 360º to do this.
As with a fretsaw, it's never a good idea to change the cut direction unless you're actually cutting material as you do so.
If you're not familiar with these types of saws, it can help to focus more on getting a good sawing action rather than following any line. The ability to follow a line will come with a little practice, whereas a faulty sawing action will throw whatever you cut out of alignment below the line you're cutting to. Incidentally, I'd rather use a coping saw than a jigsaw any day of the week: much quieter, capable of more intricate cuts and less bother to set up. In fact you can often complete a job with a coping saw in the time it takes to set up a jigsaw.