It is not absolutely necessary, but it is the most appropriate way to do it. If for any reason you can't add all the cichlids at once, then you should add the least aggressive species first and finish the process adding the most aggressive species as the last one. But don't wait too much to add the next group of fishes and complete the whole process ASAP.
About your tank's cycle, it is normal that after the ammonia comes down to zero, the nitrites go up and stay there for a while; so, be patient and you can use a bacterial additive to help the cycle to speed up a little bit.