VVTI isn't like old VVT.
For example, my car simply winds on 20 degrees more advance on the inlet cam once it's passed 3500RPM, you notice a kick as it passes this.
but VVTI is fully variable cam angle (is it?), which is part of the ECU map, so it the cam could be anywhere for all we know, maybe it tries not to use fuel for a bit, then realises you want to go fast, and tries to give you power now, hence the delay.