Like most major marriages, it was a major business contract (so to speak), and therefore little would be left to speculation. The two treaties and the Act of Parliament of 1554 naturally provide for it (as well as dowry / brideprice, Philip's titles, powers, rights, restrictions, et cetera).

In brief, there were no special succession rules. The succession would go to their various offspring according to the respective laws of each realm, and not go to the spouses.

Mary: because she had no children hitherto, their children would (as would have happened with any other first marriage) be her first heirs. The offspring of this marriage would inherit the realms pertaining to Mary.

Philip: by his first wife he had a living son, Carlos, still the heir apparent: his legitimate line would inherit Philip's lands as usual, and so long as his line continued no children of Philip and Mary would get any of these lands. Philip had no other legitimate offspring, so there were none other than Carlos in line before the heirs of Philip's marriage to Mary. So if Carlos's line died out, as usual the offspring of this marriage would inherit the realms pertaining to Philip -- in this case, those offspring would inherit both parents' lands and the personal union would continue.

A modern-spelling version:

and lest that among their children there might arise some strife for the succession, and thereby disturb the fruit of perpetual concord that is hoped shall ensue of this matrimony between the realms and dominions of either party, the said succession shall be ordered in manner and form following:

first, that as touching the right of the mother’s inheritance in the realm of England, and the other realms and dominions depending of the same, the children as well males as females that shall be born of this matrimony shall succeed in them, according to the laws, statutes and customs of the same:

and as touching the lands that the said most noble prince shall leave behind him: first, there shall be reserved unto his eldest son the lord Charles of Austria, Infante of Spain, and to the children and heirs of him descending, as well females as males, all and singular their rights which to the said prince do either now or hereafter shall belong, and shall at any time by the death either of the noble queen his granddame, or the most victorious emperor Charles the Fifth his father, (which God long defer), be devolved unto him ...; in which realms, lands and dominions the children of this present matrimony shall pretend nothing so long as the said Lord Charles the Infante, or any issue of his body lawfully begotten, do live;

but if it fortune the same lord Charles to die, and the issue of his body to fail, then and in that case the eldest son of this matrimony shall be admitted into the said right, and according to the nature, laws and customs of the said realms and dominions shall succeed: the same eldest son shall also succeed in all the dukedoms, earldoms, dominions and patrimonial lands belonging unto the said lord the emperor, as well in Burgundy as in the lower Germany

But, except for titles and honors, Philip did not thereby get any inheritance right from Mary (in contrast to the later William III and Mary II, where Billy did, by act of Parliament of that time).

and in case that no children being left, the said most noble queen do die before him, the said lord prince shall not challenge any right at all in the said kingdom, but without any impediment shall permit the succession thereof to come unto them to whom it shall belong and appertain by the right and laws of the said realm

The source I quoted above is here. It is echoed here. However, this book has not merely period spelling, but different terms, like more details of the dowry and more and different enumeration of territories. But in the matters of the succession, I don't see a difference.