popping Trinkets how long will they lastFollow

OK I hope this is not a noob question but best place to get an answer.

If I pop a trinket and say it adds 120 spell DPS for 15 secs If i then knock out all my dots with in this time do I get added DPS the duration of the trinket or the duration of the dot. And if so does this mean I can pop a trinket pop amplify Curse then hit Curse of doom to get a bigger hit on that when it goes off 1 min after.
or
Should i knock out all the dots then hit trinket and use SB to get the most out of that.