Binary self-rotation Given a binary 3D array, for each layer, cyclically rotate up each of its columns as many steps as indicated by the binary encoding of the columns of the layer above it, and then cyclically rotate left each of its rows as many steps as indicated by the binary encoding of the rows of the layer below it.
There will always be at least three layers. The top layer's columns and the bottom layer's rows should not be rotated.
Walk-through
Lets start with the small 4-layer, 2-row, 3-column array:
[[[1,0,1],
  [1,0,0]],

 [[1,0,1],
  [0,1,1]],

 [[0,1,1],
  [1,1,1]],

 [[1,1,0],
  [1,1,1]]]

The first step is evaluating the numbers encoded in binary by the columns and rows of each layer:
     3 0 2
5 [[[1,0,1],
4   [1,0,0]],

     2 1 3
5  [[1,0,1],
3   [0,1,1]],

     1 3 3
3  [[0,1,1],
7   [1,1,1]],

     3 3 1
6  [[1,1,0],
7   [1,1,1]]]

The first layer, [[1,0,1],[1,0,0]] will not have its columns rotated, but its rows will be cyclically rotated left 5 steps and 3 step respectively, thus becoming [[1,1,0],[1,0,0]].
 The second layer, [[1,0,1],[0,1,1]], will have its columns cyclically rotated up 3, 0, and 2 steps respectively, giving [[0,0,1],[1,1,1]], and then the rows are cyclically rotated left 3 and 7 steps respectively, with no visible change.
 The third layer, [[0,1,1],[1,1,1]] rotated up 2, 1, and 3 steps stays the same, and neither does rotating left 6 and 7 steps do anything.
 Finally, the fourth layer, [[1,1,0],[1,1,1]] rotated up 1, 3, and 3 steps is [[1,1,1],[1,1,0]], but its rows are not rotated afterwards, as it is the last layer.
 Putting all the layers together again, gives us the binary self-rotated 3D array:
[[[1,1,0],
  [1,0,0]],

 [[0,0,1],
  [1,1,1]],

 [[0,1,1],
  [1,1,1]],

 [[1,1,1],
  [1,1,0]]]

Example cases:
[[[1,0,1],[1,0,0]],[[1,0,1],[0,1,1]],[[0,1,1],[1,1,1]],[[1,1,0],[1,1,1]]] gives
[[[1,1,0],[1,0,0]],[[0,0,1],[1,1,1]],[[0,1,1],[1,1,1]],[[1,1,1],[1,1,0]]]
[[[1]],[[1]],[[0]]] gives
[[[1]],[[1]],[[0]]]
[[[1,0,1],[1,0,1],[1,0,1]],[[0,0,1],[0,0,1],[0,0,1]],[[1,0,0],[1,0,1],[0,0,1]]] gives
[[[0,1,1],[0,1,1],[0,1,1]],[[0,1,0],[1,0,0],[0,1,0]],[[1,0,1],[1,0,1],[0,0,0]]]
Jelly, &nbsp;18&nbsp; 17 bytes

ṙ""Ḅ}
Z€çŻṖ$$Z€çḊ


Try it online!

How?

ṙ""Ḅ} - Link 1, rotation helper: 3d matrix to rotate, 3d matrix of rotation instructions
    } - use the right argument for:
   Ḅ  -   un-binary (vectorises) - get the rotation amounts as a 2d matrix
  "   - zip with:
 "    -  zip with:
ṙ     -    rotate (the current row) left by (the current amount)

Z€çŻṖ$ $Z€çḊ - Main Link: 3d matrix, M
Z€           - transpose €ach (layer of M)
       $     - last two links as a monad:
     $       -   last two links as a monad:
   Ż         -     prepend a zero
    Ṗ        -     pop (i.e. remove the tail)
  ç          -   call the last Link as a dyad (i.e. f(Z€ result, ŻṖ$ result) )
        Z€   - transpose €ach (layer of that)
           Ḋ - dequeue (i.e. remove the head layer of M)
          ç  - call the last Link as a dyad (i.e. f(Z€çŻṖ$$Z€ result, Ḋ result) )


Note: $$ (or possibly $$ ... $$?) seems to mess up the code-block formatting (but only once posted, not in the preview), so I added a space to make my life easier.