the payments start as soon as you take a draw.
an example would be, you agree to a loan of $1,000,000 but your first draw against the $1,000,000 is only $10,000. You have to make a payment based on you borrowing $10,000 at whatever rate was agreed to.
then say your next draw is another $10,000, your next payment is [($10,000 minus principle paid)*interest rate] + ($10,000 * interest rate)
depending on how many draws you take and when, your final loan principal will be lower than $1,000,000... then it converts to a standard mortgage...
there is also a way to make interest only payments on a construction loan... I'm not familar with that.