Inside of Derived's methods, the implicit this pointer is always a Derived* pointer (more generically, the this pointer always matches the class type being called). That is why Derived::test() and Derived::get() can access the Derived::alex member.  That has nothing to do with Base.
The memory layout of a Derived object begins with the data members of Base, followed by optional padding, followed by the data members of Derived.  That allows you to use a Derived object wherever a Base object is expected.  When you pass a Derived* pointer to a Base* pointer, or a Derived& reference to a Base& reference, the compiler will adjust the pointer/reference accordingly at compile-time to point at the Base portion of the Derived object.
When you call b->test() at runtime, where b is a Base* pointer, the compiler knows test() is virtual and will generate code that accesses the appropriate slot in b's vtable and call the method being pointed at.  But, the compiler doesn't know what derived object type b is actually pointing at in runtime (that is the whole magic of polymorphism), so it can't automatically adjust the implicit this pointer to the correct derived pointer type at compile-time.
In the case where b is pointing at a Derived object, b's vtable is pointing at Derived's vtable.  The compiler knows the exact offset of the start of Derived from the start of Base.  So, the slot for test() in Derived's vtable will point to a private stub generated by the compiler to adjust the implicit Base *this pointer into a Derived *this pointer before then jumping into the actual implementation code for Derived::test().
Behind the scenes, it is roughly (not exactly) implemented like the following pseudo-code:
void Derived_test_stub(Base *this)
{
    Derived *adjusted_this = reinterpret_cast<Derived*>(reinterpret_cast<uintptr_t>(this) + offset_from_Base_to_Derived);
    Derived::test(adjusted_this);
}
int Derived_get_stub(Base *this)
{
    Derived *adjusted_this = reinterpret_cast<Derived*>(reinterpret_cast<uintptr_t>(this) + offset_from_Base_to_Derived);
    return Derived::get(adjusted_this);
}
struct vtable_Base
{
    void* funcs[2] = {&Base::test, &Base::get};
};
struct vtable_Derived
{
    void* funcs[2] = {&Derived_test_stub, &Derived_get_stub};
};
Base::Base()
{
    this->vtable = &vtable_Base;
    bob = 0;
}
Derived::Derived() : Base()
{
    Base::vtable = &vtable_Derived;
    this->vtable = &vtable_Derived;
    alex = 0;
}
...
Base *b = new Derived;
//b->test(); // calls Derived::test()...
typedef void (*test_type)(Base*);
static_cast<test_type>(b->vtable[0])(b); // calls Derived_test_stub()...
//int i = b->get(); // calls Derived::get()...
typedef int (*get_type)(Base*);
int i = static_cast<get_type>(b->vtable[1])(b); // calls Derived_get_stub()...
The actual details are a bit more involved, but that should give you a basic idea of how polymorphism is able to dispatch virtual methods at runtime.