Dwarf cichlids will not usually attack dither fish such as small tetras. I have kept Apistogramma "Ladislao" (which has quite a big mouth) with ruby tetras, which are pretty small. I have kept other Apistos as well as Laetacara araguaiae with
neon tetras and pencilfish. I have even kept
angelfish with the latter, but they grew up together, which I think probably makes a difference, so I wouldn't necessarily recommend this. Many other cichlids, such as the eartheaters for example, are not particularly piscivorous, but most may take advantage of very small fish given the chance, larger dither fish will be safe with them. Angelfish, and many acara types tend more towards predatory behaviour. Then there are those that are truly predatory like the pike cichlids, Cichla species,
oscars and several central American species that will definitely attack and try to eat other fish.
Territorial aggression is a different issue and again will depend on the species (sometimes even the individual) in question, tank size and layout etc. and whether or not there is a potential breeding situation. I haven't even mentioned
African cichlids as I don't have direct experience with them but again there are many different behavioral types..
There are 2000- 3000 known species of cichlid, with likely many more still to be described, its impossible to generalize and very wrong to say that cichlids will always attack dither fish. Many, probably most, can be kept with other fishes, but these species should obviously be chosen carefully to be compatible in terms of size and behaviour - so research suitable dither fish based on the specific cichlid species you are considering keeping.