SignatureSatori offers two options how to handle Send as addresses.
Unless you enable them in Settings, the same signature as to the primary email address is applied to them
If you enable them, you can start treating them the same way as standard users
If you don't want the primary signature applied to Send as addresses, you can enable Send as addresses but don't set a specific signature for them.
This will disable the automatic application of the primary signature but won't synchronize the Send as addresses to SignatureSatori.