What version of NiFi and what version of Kafka?
NIFi 1.x has GetKafka for Kafka 0.8, ConsumeKafka for Kafka 0.9, and ConsumeKafka_0_10 for Kafka 0.10. Whenever possible the matching processor should be used with the matching broker.
I believe all of them have some kind of property that controls the initial offset for the first time the processor is ever started, basically saying whether to start at the beginning of the topic, or at the latest offset. After that it is always going to use the last offset that the Kafka client has consumed in order to never miss data.
If you ever want to start back over at the current time I believe you can just change to a new consumer group id with Offset Reset set to latest.