So what will happen if I change to my own router immediately when the engineer is at my place?
as i mentioned, the moment a router is hooked up to the ONT, your WAN IP will change. either you do a mac clone or you use your own router's WAN IP for your live cams set up.
there is no difference in how long you hooked up the router to the ONT for before the IP is registered and tagged to your MAC.
However do note that you are not allowed to attached multiple routers to the ONT, otherwise the OLT will detect it as DDoS and your line will be disabled. What i mean is, cannot attached multiple routers within a short time, unfortunately i don't know how long apart is considered short.
Also, the system only registers 4 or 5 different IP addresses for your 4 or 5 routers. which means you will get back the same WAN IP associated to the mac address of the respective routers. Once the slots are used up, older ones are replaced with newer ones and the list goes on.
I am not sure singtel still do the above, but likely theres no change. I have been involved in testing various routers and i still get back the same old IP associated with the tested routers, so i assume there's no change. Once in a while, i do see a change in IP but there's all right i guess.