Conclusion means “should always be true”. While drawing Venn diagram you try to make the complement of the conclusion satisfiable.
For first conclusion “Some pigeons are alive” – the complement is “No pigeon is alive” → this is what is shown in the given answer and that is correct and since the complement is satisfiable the given conclusion is not VALID.
For second conclusion “Some birds are alive” – the complement is “No bird is alive” → this can’t be done in the Venn diagram satisfying the given two statements. That means the given conclusion is valid.
Your given answer is correct – just that the method is not clear.