Does an InstaLink payment confirmation mean the money is in my bank account?

No. The first InstaLinks notification confirms that your client has authorised the payment. Bank verification and settlement can still be pending, so that email is not proof that money has reached your Indian bank account.

Check the payment's latest status rather than the first email. “Paid – Settlement in Progress” means the authorised payment is awaiting processing. “Paid” means it has been credited to the Indian bank account. Compare a completed payment with your bank statement. If you later receive a failure notification, do not mark the invoice as paid based on the earlier confirmation. Keep both notifications when asking support to investigate.