Doubt regarding Chomsky Hierarchy, CFG and CSG

Question

I was following a discussion on a website, where a fellow scholar claims that this grammar

S→ aAa | bAb | ϵ

A→aA | bA |ϵ

is not CSG, so it should also NOT be a CFG. But this grammar properly satisfies the rules of CFG according me, on the other hand it fails to satisfy the conditions of CSG, which states that--

In addition, a rule of the form

S → λ

where λ represents the empty string and S does not appear on the right-hand side of any rule is permitted

So the given grammar is definitely not in CSG. But According to chomsky hierarchy

A CFG should be contained in CSG, so why this rule is NOT being satisfied for this case?