The NOTIFY without an XML body you received just after a subscription is
correct.
rfc3265 says:
This SUBSCRIBE request will be confirmed with a final response.
200-class responses indicate that the subscription has been accepted,
and that a NOTIFY will be sent immediately.
You can disable such notifies via send_fast_notify presence module
parameter.
What about further notifications. Kamailio handles subscriptions and
sends notifications when it receives PUBLISH requests.
Using terms of the rfc3856 kamailio is a "presence server" and you need
something to act as "Presence User Agent".
You can take a look at pua_dialoginfo module. I haven't used it, but its
documentation says it can send PUBLISH requests based on active dialogs
from the "dialog" module.