African cichlids can require hard water with a pH above 7.6 if they come from the Rift Lakes (Lake Malawi, Lake Tanganyika & Lake Victoria); or they can require soft water with a pH between 6 & 7.4 if they come from the rivers like around the Congo Basin.
The soft water species will be fine with tiger barbs but as mentioned by Cichlid4life, the Rift Lake cichlids should only be kept with their own kind due to the water requirements and territorial behaviour. If the tank is big enough and you have some of the peaceful species of Rift Lake cichlid you can keep rainbowfish with them, but you only want to do that with the peaceful species of cichlid.
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As for Tiger Barbs, they are renown fin nippers that should not be kept in tanks with slow moving fish or fish with long fins, and you need to keep the Tiber Barbs in groups of 10 or more.
Ruby Barbs (Puntius nigrofasciata) looks similar to a Tiger Barb but are much less likely to nip fins and the males change colour during the breeding season.