The tool is not that clever; when checking a conjunction phi&psi, it first checks whether phi holds on that state. If phi holds on the sate (as in the second example), the tool has to check next whether psi holds also on the state. The result of checking psi is then also the result of checking phi&psi (as in the second example).
However, if phi should not hold on the state (as in the first example), we already know that phi&psi does also not hold, and therefore, there is no need to check psi anymore. We can directly state that phi&psi does also not hold on the state, since phi does not hold there.
If you change the conjunction phi&psi to psi&phi, the tool behaves differently. It does not use a heuristic or so, and just checks the left sub-formula first, and then -- if needed -- the second one.