This is particularly important with ninjas. The first time many people come across this effect.
However, Ninjutsu causes a brand new creature to enter the battlefield attacking, so if you return a creature with first strike to your hand using Ninjutsu and put a Ninja without first strike onto the battlefield, that Ninja will get to deal combat damage.
702.7b If at least one attacking or blocking creature has first strike or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.
No, I am not a judge. That's why I like to quote sources such as the rules that trump judges.
"Proc" stands for "Programmed Random OCcurance". It does not even vaguely apply to anything Magic cards do. Don't use it.
Level 1 Judge as of 09/26/2013
Zammm = Batman
"Ability words are flavor text for Melvins." -- Fallingman
Does this mean that a Ninja with First Strike Ninjustu-ed in at the end of the first combat damage step will still deal combat damage during the second combat damage step?