Yes you have to put down the same depost for the children if your wanting to book them at that time. When we rebooked we booked our room and a room for my parents...we picked our rooms and made sure each room could sleep 4 people...and didn't book my neice at that time...knowing we could book her later (my parents could book her later if they decied they wanted her to go). But doing it that way we were also risking a couple things...1.) if we waited to long the ship could fill the limits of children they'll book. and 2.) the rate of the cruise could go up.
We would have probley just booked her at the same time...but the booking for my parents was a surprise...and we were not sure if they would even be up for going on a cruise...
But a simple answer to your question...YES if your booking them you have to pay the deopsit at booking time.