SoT “Refill” … How often/how much?? How does it work??

[Ydex]

Edited to add:
SoT (Sands of Time, the currency needed to launch a battle) accrues 1 per every 5 minutes. The first number is the amount you have. The second number is the maximum amount you can accrue automatically. It accrues in the background, on the server. You don't have to be logged in. Sometimes the SoT displayed is wrong. It will probably refresh to the correct number if you enter and then leave an encounter.

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Cannot find any info on how this is supposed to work.
So tried to figure it out, and here is what I’ve observed:

At 12:51 …I had… 3/120
At 1:50 …I had… 10/120 … with a 1:30 timer
At 1:52 …I had… 10/120 … with a 4:30 timer (timer has reset, but SoT did not increase)

I decided to sit and watch the timer reset and see what refills I get:

Timer reset … 17/120 (added 7 SoT)
Timer reset … 18/120 (added 1 SoT)
Timer reset … 19/120 (added 1 SoT)
Timer reset … 20/120 (added 1 SoT)

So, it appears that 1 SoT is supposed to be added for every 5 minutes...?

If that is the rate, why did 12:51 through 1:50 only add 9 SoT??
Why did 1:50 through the next reset add nothing??
Why did the next reset after 1:52 add 7 SoT in one refill??

Do you have to be logged in and have the app open in order for the refills to occur?
Do they occur at regular intervals, in regular amounts, or is this randomly generated?

Seems like there would be some info in the Help file?