The writer is from South Africa, as mentioned in the post. "Putter about" is definitely not a USAism, it's an English expression used throughout the anglophone world that can be spelled "putter" or "potter," meaning the same thing. I've only heard it pronounced "putter" personally. The stats are interesting!
I would have assumed "putter" (in this sense) is onomatopoeic, from the sound of a small engine running slowly.
"Potter", OTOH, comes from a word for poking or prodding at the ground (hence appropriate for gardening).
(I suppose with the right kind of ride-on mower, it's possible to "putter about the garden" with appropriate sound effects!)
Checking OED citations, though, it seems the "putter" form (as a variant of "potter", distinct from the sound of an engine "puttering") does have a similar history (both go back to the 1820s).
Still, I'd agree that "potter about the garden" is by far the more common usage.
Yeah you're right. "Puttering about", with that sense of a machine chugging along, seems a different thing to pottering. Pottering in a garden seems more like patiently tinkering with something than continually moving from place to place.