Does After Earth's sci-fi jargon have any basis in reality or is it complete gibberish?

First of all, I haven't seen After Earth and calling me a layman in physics would already be an exaggeration, I guess. So the following answer might be a bit vague and oversimplified (and physicists might excuse me for saying anything embarassing), but maybe sufficient for a SciFi movie.

A graviton is a hypothetical (i.e. yet to be found/discarded) elementary particle that mediates (i.e. models/represents) the gravitional force. It would thus be reasonable to say that in this case the strength of the gravitational force between objects is equivalent to the amount or energy of the gravitons exchanged between them, thus more gravitation = more gravitons. The movie thus ventures into a so called quantum theory of gravitation, a yet to be fleshed out/proved or discarded model of our world. And given the Sci-Fi context, it's not too far fetched that at the time of the movie gravitons are an established and proved elementary particle.

In addition to that, the mass is, as we all know, the charge of gravitation, i.e. more mass -> more gravitation. When speaking of "mass expansion", which I would understand as a rise in mass, the movie probably draws a bit from relativity theory, which uses a bit more complex (or "vague") concept of mass instead of the classic more stuff = more mass definition, allowing "mass" to effectively rise in certain conditions (fast travel, high energy conditions).

So the concept of gravitons and of changing, especially rising, mass is not something completely unknown to modern physics and it is not too far-fetched that both are somehow related, even if yet unclear in which way (or if at all) those theories could be combined in reality. I'd interpret that quote as meaning that a rise or otherwise measurable charge, i.e. a buildup or lineup, of gravitons has something to do with a rise in mass (although gravitation would actually be mediated by emitted and absorbed gravitons rather than actual particles "sitting somewhere in free space").

But I'm not sure if the exact causality of that quote (i.e. more gravitons lead to more mass) is completely reasonable, given that this direction seems less likely, as gravity increasing (by whatever means) doesn't need to lead to an increase in mass. But I also have absolutely no context of the scene where this is said, so maybe it was meant rather the other way around. He could mean that a rise in gravitons is an indication for a rise in mass, which doesn't sound too unlikely, given that more mass -> more gravity and more gravity = more gravitons.

So as a conclusion, even if it probably is practically gibberish and the screenwriters might not have put too much thought into it, I wouldn't downright discard it as completely ungrounded, especially compared to what other stuff is usually said in SciFi-movies and the fact that the movie neither has the goal nor the responsibility to explain every little detail in a 100% physically plausible way. But it may also be that After Earth's general critical impact (which, politely said, wasn't particularly high) or the fact that it maybe doesn't have a completely fleshed out SciFi-universe in the rest of the movie (don't know, though) might have influenced the judgement of those "many reviews".

Gravitons are still purely hypothetical, so any statement about them can be true (or false).

In physics mass and weight are two different things. Say if your mass is 70kg, then on earth on a scale you would weigh you in at 70kg, however, on the moon (less gravity) your weight will be less. The crucial difference between mass and weight is what is being measured.

Note that gravity is a force, while mass is a scalar quantity. If you are familiar with math you can say that gravity is defined as a vector, while mass is the length of this vector on earth! By definition, on earth mass = length of the gravity vector. That is way on a scale on earth you can measure your mass, however you get different results any where else and you will have to apply a conversion.

This however, does not explain why the quote is bullshit. Gravitons are (theoretical) particles that define gravity. Mass, on the otherside, is a property that is defined by the newly discovered Higgs boson ("the God particle"). To say it in a sample fashion and not entirely correct probably: If you measure weight you measure the interaction between gravitons. If you measure mass you measure the amount of Higgs bosons. So to come back to the quote, if gravitons buildup there will be a higher gravitional force, however, the mass will not change since the number of Higgs bosons remains equal.

I hope I didn't go too much into the details :)