Overshoot and ringing is the result of inductance. It’s everywhere, from PC board traces and component leads to the laser diode and its cable.
An inductor stores energy in a magnetic field. When the current changes — such as during the leading and trailing edges of the pulse — the changing magnetic field creates a voltage that opposes the change. The voltage is responsible for the overshoot and ringing, and if sufficiently strong, can damage the laser diode.
To reduce inductance, keep the output cable short, use stripline instead of round wire, ensure there are no paths to ground via the laser package, and avoid sockets, adapters, jumpers, and other connectors that extend the output circuit wiring. The video below goes into further detail.