For the record, the old rule book did tell how to resolve mulligans, you just have to decipher it a bit. The section labeled "How to start a game" gives step by step instructions on how to set up. If you read it like you are just one player, it reads pretty simple:
Shuffle, draw, place active, place bench, set prizes, coin flip, both players flip Pokemon.
In the vain of "do as much as you can" that is a common theme in Pokemon, you shuffle, draw, place active, place bench, set prizes. Now, whether you flip next if your opponent mulligans isn't exactly clear, but it is clear that mulligans must resolve before revealing Pokemon. Whether or not your opponent mulligans has never had anything to do with basic set up instructions; you still follow the instructions, they are independent of your opponent's mulligan. Common sense would say, I place my active. At this point, my opponent can't, they can reveal their hand.
I've always waited until my opponent placed their active before I've revealed a mulligan.
As for the rule change, its a bit weird. I don't see what purpose letting you decide whether or not you want to draw at the end.
More importantly, how exactly does that allow for drawing?
It has two sets of wording:
1st:
Then, the player who did not have to start over may draw a card for each additional time his or her opponent took a mulligan.
2nd:
For example, if both players took 2 mulligans, and then Player A took 3 additional mulligans, Player B may draw up to 3 cards
The first implies that cards are drawn one at a time and can stop at any time. The second implies that all cards are drawn at once and must be declared before drawing. This is situationally relevant.
I heard that at one point it was that you had to draw instantly or miss out. It also helps clear up the question of whether you can play set-up (like more benched Pokemon, or a different active) from mulligan draws, which I remember being an issue once upon a time.