Most people think Sagat mirrors back in vanilla were just about spamming TS till random factor decides.
In reality TS game has a huge part of strategy ,management and in most cases each TS determines the strenght of your next fireball.

Here are the 2 most important keys imo that allowed me to have the edge during those fireball wars.

1/ The one who gets the advantage for the next round of tigershot trade is the one who reaches later the opponent during the current trade.
2/Never more take than 1 fireball hit difference at a time (i.e. even if your opponent hits you with a ex TS , u should either trade with a normal one and get 1 of the 2 hits , or hit him with your own high or low TS at in the same trade)
Few ways to achieve this:

a/ opponent is throwing a low TS > High HP TS (the fireball has to reach the opponent after you got hit)
>Ex low tigershot
>jump=> High TS (only when u know you are in range for it to hit the opponent’s during his next low ts recovery)
b/The opponent is throwing a high TS >crouching or low TS to duck under it

Once you lose the advantage , 1 jump straight into high TS if he does low ts or a slight delay/hesitation from the opponent usualy gives you back the advantage or at least resets for the next round of trade.

Of course Kara TS makes things even harder if you know exactly when to use it . I will complete this post later.