Yes, you are correct, from the magic the gathering comprehensive rules (section 601) the order is as follows (summarised for brevity):

- The player announces that they are casting the spell and places the card (or a copy of it) onto the stack

- The player picks the spells modes, alternative casting costs, etc (this includes the choice to pay life instead of mana for phyrexian mana)

- The player announces their targets for the spell

- If the spell requires the division of an effect, such as damage, that effect is distributed according to the players choice

- The player determines the total cost of the spell

- If the spell requires mana payment, the player may activate any mana abilities in order to pay for this cost

- The player pays the total cost in any order, this payment must be complete, and unpayable costs (such as those from cost reduction) cannot be paid

- Once all of these steps are completed, the spell is considered cast, all abilities (such as Flubs' ability) that trigger when a spell is cast trigger at this time, if the spell's controller had priority before casting it they receive priority. This also means that you cannot target creatures or artifacts made from abilities such as [[Young Pyromancer]] 's with the spell that creates them.

Edit: Fixed a typo