My understanding is that the Omega (OpenWrt) has the timezone setting in the /etc/TZ file.
It can be set in the Onion Console under Settings->General Settings
I am in New Zealand and have my time zone set appropriately and /etc/TZ contains NZST-12NZDT,M9.5.0,M4.1.0/3

More information can be found about /etc/TZ and its contents at:

I don't know if the environment variable TZ has any connection or affect on this.

The timezone as in /etc/TZ (i.e. as set in Onion Console) is preserved over reboots and since recent updates is also preserved over updates