Who was filming this sequence?
The "TLI burn" was filmed by the crew of Apollo 9 - an Earth-orbit test of the lunar module. As explained in Scott Manley's video on Youtube, How Did The Apollo 11 Documentary Get Film Of The Upper Stage Ignition?, a fully-fueled Saturn V was required to launch Apollo 9. Since the lunar module was extracted before a "TLI burn", the third stage still had lots of fuel and oxidizer. The mission design was to send the third stage into a higher orbit (and eventually heliocentric) in order to get the stage away from the crew, just in case the left over propellants decided to explode.