Sorry to say, but that picture is indeed of one of the small pest types that are commonly called Majano's. Yes, some do also like to call them mini BTA's, but that they are not mini
Entacmaea quadricolor.
Just to clear some things up about 8 months ago i purchase them as BTA's.
How do majano's reproduce? do they split too or act like Aiptasia?
Sadly many dealer's (as well as hobbyists) aren't so good on ID, or even knowingly mislabel things to make a sale. Heck, you can still find stores that sell Aiptaisa covered rock as if it's a good thing to have in your reef tank.
As for reproduction, they split like
E. quadricolor, as well as quite a number of anemone species.
They like to have their foot in a shaded place and extend towards the light. They like to have their foot in a crevice. The picture he posted is a common bta color. The tentacles also resemble bta tentacles. What more do you need?
You just described dozens, if not a few hundred species of anemone from both the Atlantic and Pacific

The size these things grow to is very telling that they are not
E. quadricolor (the species commonly refereed to as BTA)
Mojano man here is your proof. A clownfish that accepted them as a host.
A clownfish accepting something as a host in an aquarium is not proof of host species. We've all seen various species of clowns accept various corals as hosts, ranging from Hammer Corals to Leather Corals. Also members of the Clarkii complex, of which EMUreef's clown is, are notorious for accepting a wide variety of non "host" anemones as hosts, including Atlantic species.