General Discussiondoes earth spirit ulti refresh when you hit said person with a remnan...

yes
or it doesnt, i always place it in a 300 radius around them to remnant
afaik it procs the ulti again as soon as its in the radius

As far as I know not immediately. The stone has to linger a bit in the vicinity to wait for the ulti refresh to check for stones in the area. I could be wrong though, but I remember that happening to me in game.

it does refresh