Browser cache refers to more than one type of object, which can include: cookies; history; and other things.
The Tablo Remote Connect cookies are the ones that are important for Tablo.
By the way, I just found the 2 cookie files for my environment.
My environment:
MS Windows 7
Google Chrome browser
Tablo Remote Connect cookie files location:
C:\Users\Radojevic\AppData\Local\Google\Chrome\User Data\Default\Local Storage
Radojevic is my username, I’m sure yours will be different. 
AppData folder is usually set to be hidden.
If you don’t know how to unhide the AppData folder, then you probably shouldn’t be messing with files within it.
Tablo Remote Connect cookie filenames:
http_my.tablotv.com_0.localstorage
http_my.tablotv.com_0.localstorage-journal
I copied the 2 cookie files from my laptop at home to my work desktop computer at my office.
I was able to connect to my mom’s Tablo from my office computer without ever actually syncing with it at her house.
Ha!