Importing a wallet (by private key or other means) does not involve any on-chain operations, and if multiple wallet instances are loaded with the same private keys, then ALL of those wallets have control over the funds of the wallet.
In a more concrete example, let's assume you have a paper wallet, that is, you have a private key saved on paper, and that the associated address has some positive balance. If you import this private key into a wallet software, that wallet will be able to spend the funds. If you import to another wallet (another software, another time, another instance), both wallets will be able to spend those funds.
The proper way to prevent control from multiple wallets:
- Create a new wallet B (and backup keys)
- Import the paper wallet key into a wallet, and transfer all funds to wallet B. This will create a transaction in the blockchain.
After this the paper wallet will be useless, as it will have zero funds left to control.
On a similar note, if I have a wallet with some funds which I want to give it to you, the 'wrong' solution is to give you the wallet keys, because then both of us will be able to spend the funds, which can lead to conflict/misunderstanding. The proper, 'Bitcoin' way is to transfer my funds to your wallet (which has different keys).