The problem with this is in the chemistry. If we assume he's correct about a plutonium-238 implosion reaction, even then we can't say for sure it had a marked effect on Jupiter's upper atmosphere because hydrogen and ammonia don't react with each other. The best case scenario would not be a cloud of soot, but a cloud of hot hydrogen and ammonia jumping to the surface, not black, but pretty much the same color as the rest of Jupiter. We'd probably see it on Earth as a little blip among thousands of little blips, each of which are hurricanes larger than North America.
According to back of the envelope astrophysics, to ignite a sustained fusion reaction in Jupiter's hydrogen core, ie, to make Jupiter into a star, a solar mass approx the size of Saturn would need to be crashed violently into Jupiter.