Mass is energy. Add energy (in any form, such as heat) to a system and you increase its mass. Thus, in the NIF reaction, the mass lost from the pellet is mass imparted on the surrounding environment. Immediately after the fusion reaction, before the energy can dissipate further as heat, etc, the reaction chamber system has the same mass as before the ignition.
There are some nuances regarding the distinction between rest mass vs relativistic mass, but they're not really relevant in this context.
I think what trips people up here is confusing mass with matter. Matter is also subject to mass-energy equivalence, of course, but AFAIU in most common types of nuclear reactions little if any matter, per se, is transformed.
