If I franchise tag a player, I won't know what his salary will be until the next season starts, correct?
I am trying to figure out how much I have for contract extensions and what my team salary will be for the following season?

Correct, when the season flips franchise players get the average of the top 5 at the position plus 20%.

I thought it was the top-5 average, or 20% more than what the player is currently making...whichever is larger?

I think it's supposed to be, but that's not how it's currently coded.