Don't you remember that Halsey mentioned there were other people there and that she volunteered to stay behind to initiate Operation: WHITE GLOVE and to ensure the Cole Protocol was enacted? The reason why Jun wouldn't be there is obvious, his job was just to see to it that Halsey got to Castle Base safely and that was it. After that, why wouldn't he volunteer or be assigned to escorting all of the remaining personnel safely from the base and helping them get to evac or a safe place to hide out? Either he and the other people evacuating found a way to get off the planet during the battle or they found a safe place to bunker down until the battle was over and the UNSC could come back and look for any potential survivors after the battle was over.

The only explanation I can think of was that there was FTL capable transport at CASTLE. However, it's still a bit of a stretch.

Because they'd then be liable to making your shit canon too. ;)