First, a clarification, connecting, with AllLinked set to $true, to a vCenter that is part of a vCenter Server federation, is not the same as running PowerCLI in Multiple mode.
In Multiple mode all vSphere Server connections that are made, are stored together in the $global:defaultVIServers variable.
All cmdlets, that do no specify a specific vSphere Server with the Server parameter, will be executed to all vSphere servers in the $global:defaultVIServers variable.
For your issue, let's first check if all is configured correctly.
Check if the configuration is saying "Multiple" for all the scopes.
Get-PowerCLIConfiguration
If you see something like this
the setting will only be for your current session.
When you stop/start the session, the setting will be gone.
You can change the setting for AllUsers, like this
Set-PowerCLIConfiguration -DefaultVIServerMode Multiple -Scope AllUsers
Then you will see this
and the configuration will be remembered between sessions.