I just performed an invite flow for one of my tenants/domains and after completing it successfully I was both able to use the tenant switcher to select that account and the original admin was also now able to see that the invitation no longer listed as pending and an additional admin is listed.
The recommendation would be for the invitation flow to be repeated; if the issue persists it may be useful to do it again and capture the steps taken so that you can include more information in the question in order to help troubleshooting.