I beg to disagree sir that you have to get the court decree reversed before your 1st wife can demand her legal standing, the law is clear:
"Art. 42 of the Family Code, the subsequent marriage referred to in the preceding Article shall be automatically terminated by the recording of the affidavit of reappearance of the absent spouse, unless there is a judgment annulling the previous marriage or declaring it void ab initio."
Thus, a mere affidavit of reappearance is required. She need not go to court.
While it is much easier to get a Decree of Presumptive Death than to get an Annulment or Decree that the marriage is void, it is wiser to have the marriage annulled. Otherwise, the subsequent marriage will be in legally complicated situation: technically, when your first wife reappears (mere recording in a Civil Registry is required), you are still married to her.
The jest in getting a decree of presumptive death is really to protect the spouse from being prosecuted for bigamy before contracting a subsequent marriage.
But well, to each his own. Personally, I would want the first marriage annulled or declared void before I would marry again. Because, really, getting such a decree will not stop from any legal complications later on: how to deal with the properties of both marriages. And the second wife is placed in a position where she cannot even prosecute for bigamy because technically, she is not married.