By the sounds of it, your plant is definitely Hemigraphis repanda (also known as dragon tongue).
If you want Alternanthera reineckii, ask the pet shop owner for it using the common name often used for that plant --red temple. It's pretty common and one of the easiest red plants to grow. The degree of redness in this species isn't dependent on nutrient levels with this one either, unlike the Ludwigias, Rotalas, et al.
Carlos