As far as I can tell, what's going on here is that there are multiple stages of antibody development. People have circulating B cells, and these cells have their genomes modified by the the VD(J) recombination process [0] from the genome in the human germline (i.e. what your germline cells and most of the non-B cells in your body have). There are a large number, but nowhere near infinite number, of B cells and corresponding antibodies that can be produced in this process, and I think these are what the authors call "germline" cells.
Once a naive B cell decides that it encodes a useful antibody (which is a complicated process), it starts to divide. Some of the daughter cells further mutate in a process called affinity maturation [1] to produce what are hopefully even better antibodies.
I think that the idea behind this research is that there are certain antibodies that can be produced by affinity maturation that are very useful against HIV, but that the "germline" B cells that lead to these antibodies are not particularly likely to be selected by the immune system when exposed to natural HIV antigens. Instead, the researchers have developed customized antigens intended to target specific germline cells which are known to be able to mature into cells that can produce the desired antibodies. If this works, the next step would be a series of additional vaccines (which are not the same as dose 1) that will try to encourage maturation into the useful antibodies.
The takeaway is that this result is very promising and that there is (so far?) no reason to expect the trial participants to be immune to HIV.
For the ML crowd, another way to think about this is that, when your body is exposed to an antigen, it runs a massively parallel search algorithm to find good antibodies in a truly massive space of possible antibodies. Unfortunately, most people, when exposed to real HIV or to prior vaccine attempts, get stuck in a bunch of not-fantastic local minima. The idea is to specifically aim the search in the right direction so, after a few rounds, it can find a better solution.