The teleperiod should be the periodic telemetry messaging for all tasmota devices, right? In other words, the periodic updates in state sent to the Telemetry "tele/" subtopic. But shouldn't the device send state changes to the State "stat/" subtopic as well when state changes? For example, with switches, you get telemetry messages every 90 seconds or so, but you get state messages instantly. Perhaps we need another MQTT Explorer log output watching one of these things to inventory the messages.
And if the device doesn't send state messages on state change by default, it seems like it would be easy to set a Tasmota Rule to send a state message upon state change for each state you want reported right away. Also, there appears to be an "Occupancy Delay" parameter that can be set through the plugin (via Admin Console). What is that set to? Is it possible that is where the 10 second delay is coming from?