Hi
Welcome to Centrify Community!
I have done some research and found the following article that might be able to help you configure the Digital ID for Adobe:
https://helpx.adobe.com/acrobat/using/digital-ids.html
https://helpx.adobe.com/acrobat/using/certificate-based-signatures.html
As you mentioned the card is able to sign you into the machine and website with no problem, I would expect this should be a configuration issue on the Adobe side. Hope the document can shed some light on your issue. Thank you!
BR,
Ivan