How to mathematically prove that a topological ordering on a cyclic graph will topologically sort its Strongly Connected Components?

Question

Let's have a standard topological ordering algorithm (from CLRS):

Topological_ordering(G)
    foreach vertex v in V do
        v.color = white
    
    for each vertex v in V do
        if v.color = white then
            Stack = DFS(G, v, Stack)
    return Stack

// DFS

DFS (G, v, Stack)
    v.color = gray
    for each u adjacent of v do
        if u.color = white then
            Stack = DFS(G, u, Stack)
    v.color = black
    Stack.push(v)
    return Stack

Now let's apply this to a cyclic graph G.

We will not have a topological ordering of the vertices of G, but we shall have a topological ordering of the graph of the Strongly Connected Components

The graph of the Strongly Connnected Components derived from the graph G is a graph in which each SCC is represented by only one vertex (also called compressed SCC graph or supergraph)

Example

For example let's look at this graph: https://i.sstatic.net/v0ORn.jpg (sorry for the poor drawing skills). In green the SSC of this graph.

Applying the algorithm above, one possible stack configuration is:

head ----> 2 ; 3 ; 4 ; 5 ; 1 ; 6 , 8 ; 7 ; 9

As you can see the vertices of an SCC are "all together". In other words we cannot have in the stack $v_1, v_2, v_3$ where $v_1 \in S_1 \land v_3 \in S_1$ and $v_2 \in S_2$.

How to prove this mathematically? Thank you.