It seems like they are just playing with the anti matter until they can figure out a way to create vast quantities of it and contain it.
Positrons (anti electrons) have been known about for a long time. The anti protons have been seen since the 1950s. Both occur naturally. If they were going to fall up I think it would have been noticed a long time ago.
For whatever reason, there are a lot of word plays in the subatomic field. Anti proton, anti electron, so according to no reason in particular, except for symmetry of word play, they must have anti gravity properties as well. But they don't, as has been seen for a long time now.
Anti neutrons are the same as neutrons except for a few small differences. One big difference between the anti neutral particles and the other anti particles is that the neutral charge stays the same, the anti part does not apply to the neutral charge.
There are other parameters for a particle's charge besides just the familiar positive and negative charges. It is those parameters where the anti properties charge comes into play.
At the macro non quantum level in normal circumstances, electrical charge is typically a surplus or lack of electrons. In the quantum world charge appears to mean something completely different.
From what can be seen, if the only difference is the electrical charge, it seems logical that a universe made up of anti particles would be the same as a universe made of regular particles. Gravity is the same for both probably because gravity doesn't care what the electrical charge is.
I would be more interested in seeing if a fusion reaction using anti particles was any different from a fusion reaction using normal particles.
There is the intriguing idea of particle anti particle annihilation of not representing the destruction of the pair of particles but instead represents the reversal of the direction in time of the particle, in that it switches from going into the future from the present and instead travels into the past or vice versa. This however is another play on words that has nothing to do with time travel, but if the surface meanings were taken as being true, it would be an interesting way to travel back in time by building a tunnel out of anti matter which you could move backwards or forwards in time with.