I concur with members who put the light as the primary factor. I'll explain, as I've no idea how much of this will be new.
First, white light is composed of colours; you can se this when light shines through a prism, or in a rainbow. Aquatic plants need red and blue light to photosynthesize, and of these red is the more relevant. All blue light for example will not drive photosynthesis. Adding green to the red and blue improves plant growth. Plants appear green to us because they are reflecting a lot of this green light.
Red leaf plants appear red because they reflect red light. Since this red light is also key to photosynthesis (which is the growth) red plants need much more red light. Intensity is the key, so that means more intense/stronger light.
With stronger light comes the need for more nutrients to balance. Adding more fertilizer provides some of his, except for CO2. In most fish tanks the CO2 produced by respiration (fish, plants, and some bacteria) and primarily by the breakdown of organic matter in the substrate, will be sufficient for low and medium light plants. But the higher light increases photosynthesis which needs more CO2 and other nutrients. Finding the balance without going high-tech (with diffused CO2) takes some effort. I would also note that diffused CO2 is now believed to have detrimental effects on fish, so one has to be careful. Actually, the increased light is not good for fish either.