You will not see a Membership Level upgraded on the member account in the WishList Member admin section until that member has logged in to the site.
If a member is Sequentially Upgraded, this will not be reflected in the Members tab in the admin section of WishList Member until the member has logged into the site. This is because the login is what triggers the upgrade.
The Sequential Upgrade is happening and is being tracked by WishList Member but it is not reflected in the Member section unless a Cron Job is used.
If you want to see the upgrade immediately in the Members section, you will need to set up a Cron Job. This is a technical process that you may need to get assistance from a programmer to accomplish.