It happens before drawing up to your reserve value. Note that it is optional. It basically allows you to dump one extra card each turn if you want to.
OPTIONAL??? Where do you see that? It looks like a detriment to balance the rest of the power cards in the set forcing you to dump a card.
I was just wondering about the timing, as with all the cards that say, "After the beginning of [phase] do [this]" that is such a vague statment.
It's optional in the way that all Actions and Reactions are optional unless they specifically say Forced (see Rancor).
While most card abilities are voluntary, some interrupt and reaction effects are preceded by the word “Forced.” Such effects must be resolved immediately whenever their specified trigger occurs as described in their effect text."
As for timing, it's pretty straight forward:
1. The draw phase begins
1b. Players may use reactions or interrupts to the draw phas beginning
2. You may discard a card
3. You draw up to or discard down to your reserve value