component.js

import Timer from 'react-native-timer'

...

render() {
  return (
    ...
    <Text>Time left: {this.state.timeLeftText}</Text>
    ...
  )
}

_startRenderTimer() {
  Timer.setInterval(
    this,
    RenderTimerName,
    this._renderTimerCycle.bind(this),
    250) // 4 times per second
}

_renderTimerCycle() {
  ...
  if (this.tmpTime !== fireIntervalString) {
    this.tmpTime = fireIntervalString
    this.setState({
      timeLeftText: fireIntervalString,
    })
  }
  ...
}

...