If you now have separate Apple IDs - which is what Apple recommends - then you also need different Me cards in Contacts. You didn't state it but has she also signed in to her own iCloud account on her phone, and is her contacts list from her Apple ID?
To select her Me card you need to go to Settings > Contacts > My Info
Then search for her name and touch on it to select it. This will identify her to the phone. If you then go into Contacts and find her name you will notice it is tagged as 'me'.
Also, check that in her iPhone the contacts are not from your account. It is possible to synchronise with contacts lists from several sources, not only from other service providers such as Google but also from another iCloud account.
Go to Settings > Contacts > Accounts.
If your iCloud account is there it should be removed if you wish to have separate contacts. If it is present it will have the capacity to edit the contacts over on your iPhone.
How did you copy the set of contacts onto your wife's phone?