I'd advise against adding tetras, or any typical community fish, to a cichlid tank. You may find the one odd occurence where it'll work, but it's not very likely.
I had a friend at work selling a 55-Gallon, complete setup (tank, stand, fish, etc.) so I bought it from her. When I went to see the tank, I stared in amazement at his selection of fish. 2 fully grown Jack Dempseys (one of which looked to have a broken spine...) 2 Baby Common Plecos, an "eel" of sorts that measured all of 5", and...a Black Skirt Tetra.
Yes, a Black Skirt Tetra.
According to the lady's son (who kept the tank) the tetra had been in the tank for years and got along famously with the fish. I thought "Eh, ok...wonder why, but whatever."
I got the tank home and added the baby South Americans to the 55, along with the fish that occupied the 55-Gallon under the previous owner. Including the Black Skirt Tetra (which I really should have found something else to do with...)
Within 2 hours, the Black Skirt Tetra was met his demise at the fins of a Dempsey. One of the same Dempseys that he had previously been housed with.