Random ticks do not appear to occur on blocks which are loaded by a nether portal based chunk loader. I have tested this with grass growing, both on a server and in single player, both with my player far away in the overworld, in the nether, and offline, and in none of those cases did the grass grow.
To Reproduce:
Open a new world, and go far away from the spawn chunks.
Create a portal-based chunkloader.
Type /gamerule randomtickspeed 0
Create a grass block surrounded by 8 dirt.
Teleport far away.
Type /gamerule randomtickspeed 1000
Wait a few seconds.
Type /gamerule randomtickspeed 0
Teleport back.
If the mechanic were working, the grass would have grown; however it has not.
Environment
Overworld
It’s dark in your screenshot. Grass needs light to grow.