As has been said it looks to be a bacterial bloom, most likely due to elevated nitrate levels; that's my guess. I say that because you said you have a problem with algae which one of the contributing factors in an over abundance of algae growth is elevated nitrate levels. Nitrate levels can become elevated due to over crowding, overfeeding, the sudden addition of more fish then the already established biological filtration could handle or insufficient filtration. Any of these factors can cause a sudden bacterial bloom, if it's the addition of fish, water changes and time will help the bacteria to establish themselves in the proper levels to deal with excess bioload as long as it's within reason.
Interestingly enough what probably helped keep your water clear was the algae you scrubbed off as it was helping your biological filtration by consuming the excess nitrates. I believe the algae made up for the lack of biological filtration you have by keeping the tank so barren or not having the right amount of certain filter media or a small filter size. In my experience a barren tank needs better consideration in its filtration system and it's media and better consideration of the tanks occupants to help keep the nitrate levels in check. This is because the addition of ornaments and substrate creates more places for the biological filtration that consumes nitrates to establish themselves. One of the reason they help is because nitrate consuming bacteria is unlike bacteria that consumes nitrites and ammonia which like oxygen rich environments, nitrate consuming bacteria thrives in areas of low oxygen. So it will grow and thrive under the sand or under tiles and in the porous parts of ornaments that don't get much water circulation creating a secondary home for the bacteria outside your filter; which of course more is better as more of them can handle a larger bioload.
Sorry if that was long winded, just figured it was worth explaining, which by the way might explains why your other tanks are stable. As for how to fix it we first have to figure out for sure what the problem is instead of me just guessing. Do you think you over feed? How often do you feed? What kind of filters are you running on the 135 and what kind of media are you using? How long do you leave your lights on for? Does the tank get any sunlight?