How do sims handle double on-use trinkets?

Position matters when using two On Use trinkets (with one big exception). The trinket in the top/1st slot will be used first and the 20 second delay will be handled before using the second trinket.

This order can change how a trinket lines up with bloodlust, cooldowns, or the length of the fight.

In Droptimizer, this can sometimes result in surprising trinkets being listed as upgrades. The reason is sometimes because of the trinket order and if you swap the better trinket to the first slot it may make more sense.

In Top Gear, this can sometimes be seen in results where your trinkets are swapped around in order. Top Gear will try items in both slots in case one of them lines up better with the APL.

The big exception is if your class APL has custom handling for specific trinkets. If there are particularly powerful trinkets, class devs will often ensure their usage is handled explicitly in APLs. In this case, the order will not matter but Raidbots will still try in both positions. This situation will show the two trinket orders as pretty close in DPS or as sidegrades.