I've transplanted my little seedlings into their peat pots. They seem to be doing well now, although there were some mistakes (I forgot to soak the soil of the first pot of seedlings, and as careful as I was, the soil was so dry and lumpy that I ripped off some of the root system. The rest of the seedlings I soaked with water first, and the earth fell off the roots nicely).
I'm SO glad that this little image was on the packaging for the peat pots, or else I think I would have totally freaked out if I started to see roots growing out through the pots! I assume that it's actually normal peat pot procedure. :)