In the reference page for glMemoryBarrier, the descriptions for GL_ATOMIC_COUNTER_BARRIER_BIT and GL_SHADER_STORAGE_BARRIER_BIT are these, respectively:

GL_ATOMIC_COUNTER_BARRIER_BIT
Accesses to atomic counters after the barrier will reflect writes prior to the barrier.

GL_SHADER_STORAGE_BARRIER_BIT
Accesses to shader storage blocks after the barrier will reflect writes prior to the barrier.

However, in the OpenGL 4.6 (as well as 4.3-4.5) core specification, the descriptions of these are longer and include some important information about the reads becoming visible (emphasis mine):

ATOMIC_COUNTER_BARRIER_BIT: Memory accesses using shader atomic
counter built-in functions issued after the barrier will reflect data written by
shaders prior to the barrier. Additionally, atomic counter function invoca-
tions after the barrier will not execute until all memory accesses (e.g., loads,
stores, texture fetches, vertex fetches) initiated prior to the barrier complete.

SHADER_STORAGE_BARRIER_BIT: Memory accesses using shader buffer
variables issued after the barrier will reflect data written by shaders prior to
the barrier. Additionally, assignments to and atomic operations performed
on shader buffer variables after the barrier will not execute until all memory
accesses initiated prior to the barrier complete.

Curiously, the other barrier bits in the reference page include this information.