During the time that both will have coverage, primary would be to whichever partner is older, and secondary would be the insurance company of the younger spouse. I would recommend informing both companies, so they will know if they are going to be secondary or primary, which will help on invoice and refunds. Other than this, there aren't any implications that come to mind.

Health insurance is always helpful i think their is no harm in taking dual health insurance policies. I too got one from Apollodkv and my spouse as well.