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Let's say I have a wallet in my computer and I create an address so another person can deposit bitcoins in it.
Then it is passed to miners and later added to the blockchain. But in the meantime this transaction was not verified.
When does my wallet is updated so the balance in my wallet and in the other person's wallet are correct?
Does my wallet (and the other person's wallet) go check if it is finished and validated?
your question is unclear on verification. I think you are asking for this process: You create an address, give it to your friend, he creates a tx, and sends it to you. At this point in time the transaction is not yet mined, but you anyhow get within seconds a message, saying someone sent you some funds.
In the background the wallet software is constantly looking for updates on the network, and here for s.th. like "my address". This eventually triggers the "funds sent to my address" message on the wallet. At this point in time it is unconfirmed. Roughly after 10minutes it should get its first confirmation, which means it is also included in a block (and verified in all details).
SPV wallets don't do verifications in the same way as full nodes. Full nodes verify each transaction, as described here.
you should wait for the confirmation time of it. if it was accepted by the blockchain then yes, it'll be confirmed and will be broadcasted shortly.
