Plasma, by definition, is the state of matter such that some or all electrons are removed from the atoms. It is sometimes referred to as the fourth state of matter (after solid, liquid, and gas). So, you are correct - plasma contains charged particles, ions and electrons, rather than neutral atoms. Plasma could be produced by electrical discharge, or application of a strong magnetic field (Please see the reference link).
During a fission reaction a large nucleus breaks apart into smaller nuclei, and energy is released in a process. I am wondering if your friend read somewhere that the resultant mix of nuclei and neutrons can be referred to as "plasma", but I have never heard this, and this would not be the same kind of plasma as described above.
The confusion also might arise because plasma is often mentioned in connection with a nuclear fusion reactor. (Notice, fusion - not fission. During a fusion reaction, two small nuclei bond together into one, again, with release of energy, which is much greater than during fission). The temperatures needed to produce fusion reactions are so high that the matter would be in the state of plasma. Explore the second reference link to read about different ways the plasma can be managed in the nuclear fusion reactors.