I have had success with just feeding regularly with table shrimp and I dose the minerals in my system with the balling method and my BTA is very health. I fact the guy just split two weeks ago.
I don't know about food related to changing the colors. But I would think that different lighting would play a bigger role in the coloration. When I bought my RBTA from a local shop it was a real dark rose red under there ecotech led lighting. Fast forward to over a year later and under reef breeder LEDs, mine are more vibrant green at the base and translucent reddish tips. Feeding them a variation of scallops, LRS, Rods and now Jimbos reef food has only caused them to grow and split.
Someday I would like to take a tank and try different lighting patterns to see what if anything would change the color of these BTA's.
I had a rose one before and colored it up using Pro-Salt Krill. If I remember I was feeding it 1 krill about every 3-4 days. If you have any Cleaner Shrimp make sure to feed them at the same time so they will leave the anemone alone to eat.
The reason I ask is that my dispaly has 3 large RBTA's. They are gorgeous red with a green center. One of those split, so I moved it to another tank where it crawled out of the critter keeper and long story short I have 5 RBTA's in that tank now. But no green at the base. I also feed that tank differently, and that tank has different lights.
The display with the gorgeous anemone is T5's. The 5 blah color ones are under Ocean Revive LED's. I started target feeding the 5 nems about 3 weeks ago with mysis but no color change (but lots of growth). It's been about 3 months since they split.
Meantime the ones in my other system have never been target fed and are amazing. I want all of mine to be amazing. I know others with my same lights and light settings that have great color. All other parameters the same that I know of (not testing for stronium or things like that).
When I kept anemones good water and light played a huge role in keeping them looking hot. Aside from that krill worked the best for me. The color was much better IMO
I have decided to try injecting my table shrimp with ammino acids and see if that helps further with the coloration and healing (since I propagate them)
Hoping it works. The first feeding did go well and the Nems showed some yellow for a second, but I am sure that was just the AA being squeezed out of the shrimp. Not sure if they are absorbing it or not, but for that second they look really good
Lighting has the largest factor overall in coloring for bubble tip anemones. Greater intensity with a good specteum of say the 14K-20K range plays along with more vivid colors and then lower intensity tends to be duller coloring as well as with less UV’s and Blues too.
As others have mentioned, feeding tends to just make them split more overall more than anything.
I concur that lighting plays a key role in the color of an anemone. Anything other than that -- such as food -- has minimal effect, if any. Keep in mind that anemones don't need to be fed, and it's not their primary source of nutrition.