That is how a rocket achieves enough speed for a transfer orbit. For SpaceX specifically, the second stage reaches LEO, then, if the satellite like Starman wants to go beyond LEO, they fire the engines to put them in a transfer orbit about the Earth or Sun. If a satellite wants to go to Geostationary or Geosynchronous orbit, it has to achieve apogee, where the the engine is turned on for a second time to circularize the orbit. If a satellite wants to go to interplanetary space, then the rocket has to achieve orbital velocity, then escape velocity by turning on the engine for a second time, which can put them into an elliptical solar orbit. This is called a Hohmann transfer. Some satellites like New Horizons don't turn on their engines for a second time, but rather achieve escape velocity of earth in one long burn. SpaceX does this for Geostationary transfer orbits, but not for interplanetary spacecrafts; they first achieve parking orbit.
Most of the missions you've listed in your question are either interplanetary spacecraft (like Emrites Mars Mission: Hope or Starman), or are geostationary spacecraft (like JCSAT-16). So a second (and sometimes third depending on the rocket) burn is required.
The recent Starlink launch though is a not Geostationary nor interplanetary but rather LEO. According to Spaceflight Now Falcon 9 Starlink timeline, the second burn is required to circularize the orbit. It should be noted that the second stage was ignited for a second time very briefly (2 seconds).