A wave packet approaches a finite potential barrier. Classically, a particle with too little energy would turn back; quantum mechanically, the wave penetrates the barrier and can leave a transmitted packet on the far side.
The barrier height is compared with the kinetic energy of the incoming packet. When E < V0, the wave inside the barrier becomes evanescent instead of abruptly stopping.
The visible density is the Born density. Reflection and tunneling are two parts of the same evolving wave packet.
Bohmian particles have definite positions, but their velocity is guided by the quantum current. Some trajectories are carried back by the reflected wave, while others follow the transmitted branch through the barrier.
The Pauli option adds a spin current, changing the detailed paths while the same density still determines the reflected and transmitted probability pattern.