When inviting your customer's tenant to your own Teams tenant via Teams Connect, your customer's end users will receive a notification in Teams under their Activity Feed.
This will open a window which asks them to sign in and approve a list of permissions.
Once the end user accepts the permissions, they will be able to chat in the Teams Connect channel you have set up.
Alternatively, the end user may also see the new Team and channel in their Teams sidebar where the rest of their channels are usually located.
Opening the Teams Connect channel there will trigger the same sign in flow as above.