Phase 10 - Can you hit on the same turn as playing a phase?
I don't have the rules in front of me but I have always played that you could play on other players right away.  

I could see that argument in a 2 player game that going down second would have an advantage but if both players are playing that way it is more likely that your opponent will just go out when they put down their phase and therefore stopping you from playing your phase and sticking you with a lot of points.  I would argue it better to move on to the next phase and get a small amount of points then not to go down at all.