Definition of the Decryption oracle
In the standard definition of security for public key encryption schemes there exists only one public key.
Therefore the decryption oracle will always decrypt with the secret key that corresponds to the public key given to the attacker. It does not matter how the $c_1$ in your question is computed, it can be computed using the real public key, a different public key or might even be random garbage. The decryption oracle doesn't care, it simply runs the decryption algorithm with the secret key produced earlier in the security game and the input provided by the attacker.
Whether this results in a valid decryption or not depends on the encryption scheme and is not part of the security definition.