I think you answered your own question.
Just an example: If I earned 1$ last month, the authority would pay me 0.25$, and the authority would transfer me the token ‘storj’ equals 0.25$ in 7th. The price of token ‘storj’ varies with great ranges. The price of the token ‘storj’ is average 1$ on last month, is 2$ on 6th this month, is 1$ on 7th this month. How much can I get the token ‘storj’ at the end?
The distributed sum is converted to STORJ on date of sending, so sent $0.25 will be received as $0.25 in STORJ tokens.
The amount of STORJ tokens depends on rate on coinmarketcap on sent date.
Since the market changes constantly what it says on the dashboard is what you got at time of payout, But storj price might have dropped or increased it all depends on the market.
With the recent change to send rewards over a few days if fees drop, are those calculated at the same time or will it be calculated (roughly) at the point of the transaction?
It’s updated nearly the point of the transaction.