Imagine a particle with energy $E$ heading towards a potential step with height $V_0$ where $E<V_0$. The particle's wave function is oscillatory before the boundary and exponentially decaying in and after the boundary. However, there is still a small probability the particle can be found in the 'forbidden' region. Is this quantum tunnelling? I read that for a potential step like this, there is a 100% reflection so I'm getting getting the indication that there is no tunnelling.
It is quantum tunneling if the step potential has finite length. In this case, the continuity conditions on both sides of the step potential will show you that there is a nonvanishing amplitude behind the potential. If the potential has infinite length, there is no space to tunnel into.