When the hub is connected to the host and there are no devices plugged into the downstream ports (no bus activity in the downstream ports), the host will issue a suspend request and the hub will be suspended. In suspended state the TetraHub will draw about 100 uA as specified in DC Electrical Characteristics section of the TetraHub Datasheet. Hence you see a drop in power consumption when plugged into the host.
Section 188.8.131.52 of the USB 2.0 Spec states the following
This state is entered when:
-The 3 ms timer expires in the ReceivingJ "
This J state for a continuous 3 ms is interpreted as a suspend signal by the USB device. Having the device unplugged may not (most likely not) cause the hub internal logic to detect a suspend signal. It is the lack of activity and a constant IDLE (J) state that signals a suspend event to the device which in turn causes the hub to go into low power mode.
When the TetraHub is not connected to the host but is in a powered state, the USB datalines D+ and D-are floating. The Hub must detect a suspend signal (J state for about 3 ms) in order for it to go into low power mode. Since the D+ and D- are not in a driven state (J), the hub does not see a suspend signal, and it does not go into low power mode.