Gluing underwater is best done with epoxy putty and/or super glue, preferably gel or thick. The putty can cure underwater just as it does above (i.e. it requires no oxygen) and doesn't release any toxic byproduct underwater and likewise with super glue.
In some, if not most, cases epoxy putty alone might not stick well. If that is the case, then using the putty in combination with super glue gel works well. Super glue gel dries by reaction with water. I use the gel because (a) it dries slightly slower, although you still only have seconds under the water, and (b) it has some gap filling ability in case you don't have a perfect fit for the two surfaces you are trying to glue, although I still recommend a perfect fit if you can. You'll want to apply the super glue above the water and then quickly attach it to what you want. You'll only have seconds to work with it once it's under the water, so get ready to rush to position.
Sometimes I use the putty not as an adhesive but more as a mold using the superglue as the real adhesive. For example, I'll use the putty as a clay sort of between the rock and frag setting it up just as I want it underwater. Then if the putty didn't stick--and it often doesn't--I take it out, carefully noting where it had been in the tank, pat the putty dry, and apply super glue gel liberally on the surface that must stick to the rock. Then I quickly stick the putty back into the tank and position it on the rock exactly as before using the impression of the rock that is now on the putty. You only have seconds to work with here, so position it quickly. The epoxy should stick, but if not, just redo it until it does. Now, take the frag out of the tank, pat dry the end that you want to glue, put super glue gel on that end, and again quickly stick it in the tank and into the impression of the frag end made in the putty earlier. The keys are that you have to do everything relating to the super glue quickly and need impressions, both rock and frag end, in the putty for the superglue to work well.
