You have started to play with the Template Signatures, however, what you defined and assigned is not added to emails sent.
Although it is not very clear at the first sight, a Template Signature is a global signature as well.
Global signatures could be assigned via Client Options -> Send -> Global Signature.
Here you can set Global Signature or Template Signature, but not at the same moment. Then you are assigning two global signatures which would not work.
When you choose any item from the Global Signature menu option, set then Template Signature to None. Or vice versa. If you choose and want to test Template Signature, you must set Global one to None.
Needless to say that this is a client setting option that needs to be applied to account(s) by a POA and afterwards, when a user logs in such mailbox, only then the client re-reads new settings and applies them.