If the tuning was EADGBE before and you took all the strings off, put them back on and retuned to EADGBE (with same gauge strings) you most certainly don't need to put extra springs in there, or in fact, do anything to the springs. The string tension is the same if the tuning pitch is the same. The trem angle should be the same as well.
Uh-huh. My post supplemented the ones above that suggested tightening the claw if needed.
To summarize: "Greg, if he hasn't changed his tuning, he shouldn't need to adjust his springs. On the other hand, it sounds like he HAS adjusted his tuning, in which case he will need to adjust the springs possibly as part of a complete setup."
So, since you're indicating that he might need to adjust his springs... my advice would be...
"If that turns out to be the case, and you find that while adjusting the springs, you can't tighten the claw any more, you also have the option of adding additional springs to increase tension on the trem block."
Around and around she goes....