Typo in the event name.

inline_states => { ...
    Send_updates => \&send_update,
...

# later
$kernel->yield('Send_update');
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Correcting that leads to a newer problem, though.

a 'Update_clients' event was sent from pmtest.pl at 57 to session 2 (T
+OF) but 
session 2 (TOF) has neither a handler for it nor one for _default
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But the event names look correct in this case, so InlineStates must not behave the way you expect in this component. Looking at the source for POE::Component::Server::TCP it seems the InlineStates are not added to the 'listener' PoCo::Server::TCP session, but only to sessions spawned by the default Acceptor handler which is used when one is not provided by the caller. In any case, the session 'TOF' would not get the InlineStates, it's children would. There doesn't seem to be an easy way to add additional states to the listener at creation. But I only took a quick look at the source.