As
@fenderman says - many IP cameras that claim ONVIF compatibility may not even implement the mandatory aspects of the ONVIF specification, and probably haven't had certification testing.
Last time I looked - and I'll admit it was a while back - 'push/pull event subscriptions' which would be used for triggers such as motion detection etc were an optional part of the ProfileS specification, so not often implemented.
The only IP cameras that I have seen so far (maybe 6 or 7 brands) that support motion etc events under ONVIF are Hikvision. But they do have a real ONVIF certification, which generally you won't see on the low-end brands.
There is an easy way to see if the cameras support motion detection events under ONVIF.
Use the very good Windows open-source tool 'ONVIF Device Manager' from sourceforge.net
Let it find the camera, and take a look at the 'Events' page.
Create some motion, and see if you get anything like the Hikvision sample below: