This is one of the biggest misconceptions that make me cringe whenever I hear it, no offense to you just one of those peeves I have. The big bang was not a "bang" at all, nor did it have much to do with matter, except that it was evolving into a more stable form. But, rather it was *space and time* that was expanding and as a result matter and energy "cooled" In addition the theory of dimensions be created continuously after the big bang is folly, again no offense intended, all of the dimensions we know of, experience, or theorize were created *at* the big bang through initial conditions which also determined the power of weak and strong nuclear forces, gravity, and electromagnetism
Misconceptions work both ways. Dimensions, unfortunately, can mean the length, width, depth, spazitude, etc of an object, but it has a LONG tradition of being used as meaning an alternate reality as well. Both uses are technically correct. Home World and Another World are two dimensions that exist in the same dimension, as it were (that is, two 3-dimensional worlds that are separated by a 4th dimensional distance... or 4-dimension worlds separated by a 5th dimensional distance, or something like that).
Anywho, on the topic of dimensions I do recall the possibility of energy (and matter) existing simultaneously in all possible dimensions (I'm trying to track down WHERE I heard this, so far with no luck, so it might have just as possibly been something I read on a different forum, in a sci-fi book, or heard in a physics class). Consider the Double-Slit Experiment; by all appearances, a single photon can pass through two different slits at the exact same time, striking a photographic plate in two different locations (well, more than two locations, really; if there is only one slit, the curious outcome disappears, and if the photons are measured as they pass through one slit or another the effect disappears) . This may be the result of that photon existing in different locations at a single time. Extrapolated from that, it might be possible for a photon (and matter in general) to not only exist in two 3-dimensional locations at once, but also two 4-dimensional locations. To offer an example, the energy and matter that would comprise the Masamune in Homeworld would be the exact same (not just similar, but the exact same) energy and matter that would comprise the Masamune in Another World. Energy and matter would seemingly be limited, but their potential locations are not (sort of like how money is limited by wealth isn't).
Thus, when dimensions split no new matter or energy is created and neither is energy or matter divided between the two.
As for how dimensions are created, it seems to be a very rare event in the Chrono Universe. Possibly they normally exist independently from the very beginning of time and that splits never (or should not) occur. Alternately, the p-value for splitting dimensions may just be very high (or would that be low… meh, whichever one means unlikely – I apparently need to refreshen my memory on p-values).