What is the actual file type? I ask because vcards are not the same as information saved for/from contacts. Well, not all of them anyway.
Some are just virtual business cards. Which are not always readable by all devices.
The ones that save contact information from your phone are vcf files (example... filename.vcf). Those are the ones you need to be able to transfer them over to your phone. You can also create them on your phone to copy elsewhere.
Check the files you are trying to access and make sure they end in a vcf extension. If they don't, you may have to manually input the info onto the phone.