I've seen it before, but only three times that I can remember, out of probably close to a thousand tanks I've maintained and/or seen over the years. If I recall it was also accompanied by a white slime.

It's definitely not an algae. 

I'm pretty sure it's a type of fungal/mold growth and that it may also involve bacteria, hence the slime. From my experience and the experience of other tank maintenance professionals, it starts most often in doctor and dentist office reef tanks, probably because of the unique chemicals that are used (everyone knows the unique smell of those offices). 

We dealt with the problem using Dr. Tims Waste Away for Reef Aquariums. It wasn't a quick fix, but over the course of several weeks and watching it closely to ensure that all other tank conditions were kept healthy, it finally went away. Extra water changes were not required.

About the Refugium, yes, any cheap little pump will move the water just enough and that's not a bad idea, but I'm not convinced that is the real issue. That is, if I'm right concerning that ball of Chaeto with hair algae. 

First, 5000 Kelvin is inefficient yellowish lighting for reef organisms. It grows hair algae better than anything. I would replace those 3 LED's with one(1) Home Depot Special. One will do the job but feel free to splurge and buy two.  The HD Special is so named because the cone reflector and the highest wattage "Daylight" color twist PC/CFL bulb (abt 30 Watt) can be purchased at a hardware store for about $17. Get the ordinary twist PC bulb, not the flood light and make sure it is the Daylight color.

Secondly, I'll bet that snails or hermits in the Refugium are few in number. Without adequate numbers of those little workers, those little Reef Janitors, hair algae becomes an UGLY GREEN HAIRED MERMAID (click to read the story). After the hair algae is managed, the Macroalgae can take over the whole job of eating nutrients. 

Hope this helps.

Aloha,

Mark  

P.S. 

A spray bar diffuses the flow. Little streams of water "spitting" out all those holes cannot do the job that can be done when that same pressurized water jets across the tank from just one appropriately sized orifice/tube.

In the pics, which I assume is the Refugium(?), I see what looks like a ball of Cheato that is covered in hair algae. That ball of mixed algae is cleaning the water but it can also lead to trouble. In all my experience, hair algae grows for three main reasons; 1) not enough Snails and Hermits to eat it, 2) the spectrum of lighting is too yellow, 3) it took over when Macroalgae such as Caulerpa, was removed or died. I'm sure we can provide some more sensible recommendations about making improvements to that Refugium, like simply using a small powerhead placed in bottom center pointing up. The algae does not have to tumble to be effective and snails and hermits are useful in the Refugium too. Also, are those Halogen lights?

Okay lets also talk about the other issue, white hair algae in the Display Tank. Please forgive me but what is white hair algae? I don't know of any algae that is white, unless it is dead. Chlorophyll is not white. My google searches turned up threads about it in freshwater forums not saltwater forums. It was identified as a fungus. So what is this stuff in your reef aquarium and is it a bad thing or a good thing? 

Could it be a type of Sponge? If so, that's a good thing because it adds to overall biofiltration and stabilizes the tank. Sponge is a beneficial marine animal.  

Could it be the mold that grows on decaying organic matter from LR. If so, that's a good thing in the short run. Mold is, well, a mold/fungus, not animal nor vegetable, but still beneficial. 

Could it be dead hair algae or dead Bryopisis algae? If so, that's a good thing, but we ought to ask, "Why did it go white?"

If you wouldn't mind, please post some pics so we can ID this stringy white stuff for you and offer recommendations.

Aloha,

Mark  

P.S.

I'm told that my comments can sometimes come across as condescending. Please forgive me. I mean no disrespect. I'm just trying to use what I know to offer some help.