If the test email you sent to ******@domain2.com was received by the account, you likely already have that alias added. But there are some other methods that can be used to ensure that messages are being delivered to the "correct" recipient.
If you are familiar with PowerShell, you can confirm this by running the Get-Mailbox cmdlet, like this:
Get-Mailbox ******@domain2.com | select -ExpandProperty EmailAddresses
and in case the above query returns nothing, you can double check via
Get-Recipient ******@domain2.com
That second cmdlet will return any object within your tenant that might have the alias configured on it.
Another thing you can do is run a message trace and check the detailed information therein, it will tell you how/why the message got to the final recipient. Here's the relevant article: https://learn.microsoft.com/en-us/Exchange/monitoring/trace-an-email-message/message-trace-modern-eac