The Ecosystem filters are a Hang on Back type of "refugium"and as such you could do a search on "refugium"-"fuge" for other general information and experiences.
In general a "fuge" will help with a hair algae/micro algae problem by allowing the growth of "macro' algaes which will compete with (and hopefully beat) the "micros" for nutrients in the tank...
In principal the "Ecosystem" should help your tank, but the ones advertised are rated for 40-60 gal tanks and you have a 125...
Unless you are planning on purchasing two or three units for your tank it may not put but a dent in your algae...for that kind of money (or less) you could build, or have built, a much larger system with over flows and return pump for under or over your tank.
(In My Opinion)...A fuge is a good thing and will help your tank...But this one in particular may not be the "best" choice for your system.