I asked an identical question a few months ago. I'll try to explain it as it was explained to me;
Bob is the maintainer of the "original" software package licensed under the AGPLv3
Alice made a private modification in which no remote usage was given
Joe is a user of Alice's version, used to serve a app on his public site
Since Alice did not provide interactive access to a remote user, AGPLv3 section 13 never came into effect. Since Joe did not modify the software as he received it from Alice, under normal circumstances AGPLv3 would not seem to apply to him either.
If Alice distributed her modifications exclusively to Joe, such as a contracted work, she also need not comply with the GPLv3 terms under section 2:
You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force. You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright. Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.
Note, however, that in doing Joe is the one making the modifications via their exclusive arrangement, and thus AGPLv3 section 13 applies to him. Bob can ensure this as copyright holder.
If Alice and Joe had no exclusive arrangement, Alice would have distributed her modified copy to other people, in which case her work (in most cases) would already be available.
In either case, Bob's goal of ensuring the availability of modified versions of his software should be met. It's of course impossible to cover every potential scenario. The FSF has said that they expect more frequent license releases as the need arises.