Just a guess but I think it probably means that either the device itself or the Zigbee gateway/bridge/hub or its integration only uses “Local Polling” or “Cloud Pulling” instead of “Local Push” and “Cloud Push”.
https://www.home-assistant.io/blog/2016/02/12/classifying-the-internet-of-things/#classifiers
Also, I think that a problem as the Sonoff Bridge officially only supports other Sonoff branded devices, so it is not like you can contact Sonoff/Itead and ask them to fix this problem with third-party devices.
Just because a device is Zigbee does not mean that a proprietary Zigbee gateway/bridge/hub from a commercial company will support it. In fact, most proprietary Zigbee gateways/bridges/hubs from commercial companies will only support their own devices and/or devices from select third-party partners that they made a deal with to support.
Good luck with that, as the reason why people (like myself) will recommend that you instead buy a modern Zigbee Coordinator USB adapter and use it with Home Assistant’s own ZHA integration or with Zigbee2MQTT is that either/both of those two Zigbee solutions are capable of supporting all different brands of Zigbee devices made from practically any manducates.
The Zigbee specification is more of a guideline than a strict set of rules that device manufacturers have to follow, and that makes it hard or at least a lot of work to offer support for untested devices as many devices will need some kind of custom converter/parser/translator to workaround unique Zigbee clusters and attributes that the firmware developer of each device has decided to use.
So going against your hope I am going to recommend that you buy Home Assistant SkyConnect dongle (based on Silicon Labs EFR32MG21) for the ZHA integration or ITead’s “Sonoff Zigbee 3.0 USB Dongle Plus” (model “ZBDongle-P” based on Texas Instruments CC2652P) for Zigbee2MQTT.