I don't think it always necissarily needs to be tumbled as long as it's getting good flow through it. From my understanding of what other hobbiest are saying is that it has a tendancy to collect deitrus without good flow. So idealy good flow and tumbling would be best. But I think as long as it gets flow and you hand tumble it every now and then you'll be fine. Also the tumbling allows light to penetrate inside the ball better from many angles to help help it grow faster and prevent die off which would leach of nutrients back into the tank.
A couple of sources....
overview
Chaetomorpha Algae, also known as Spaghetti Algae or Green Hair Algae, is an excellent macro algae for refugiums. Each cell grows end to end, creating long, stiff strands. It grows in filamentous clumps, resembling a ball of fishing line. This algae is fast growing and is not palatable to many herbivorous species.
Chaetomorpha Algae removes both phosphates and nitrates from the water. To increase the amount of nutrients this algae exports, use moderate to high lighting and keep it in an area of high water flow. It should ideally be tumbled in an algae filter.
Chaetomorpha
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Availability
It has a natural distribution range throughout Australia, yet it is under-utilized in Australia in favor of other macroalgae and other nutrient removal techniques.
Use[/b]
A cheap, energy saving globe with a low Kelvin rating (5000-6500K) can be used to maximize growth. Cheatomorpha should be 'tumbled' with good water flow to prevent other less-desirable algae from settling on it.