Here's a wild guess. The Vault may have encrypted the protected files to be used only with the previous phone. So if you try to open them in another phone (assuming you have installed the Vault with the same Google account), the new phone won't be able to access them.
I have emailed email@example.com regarding this issue. Hopefully, they will reply. I will then update / confirm this answer. If not, it's safe to say my assumption was right.
Thank you for contacting NQ Mobile Customer Support!
You would not be able to show pictures on your SD card in another
phone. Once you put them in Vault they are encrypted in the phone and
would not be able to be seen. The Vault application is specific to
each phone unless you transfer the application to another phone.
Thank you again for contacting NQ Mobile Customer Support!
NQ Mobile Customer Support Team
What can do is put back the card into the old phone, and remove the protection from the Vault. I'm sure you can un-protect pictures, like in other apps. After you've unprotected all the pictures / files, put back the SD card to your new phone. You should be able to read the files. After that, you can protect them again using Vault (on your new phone).