Here's how signings work.
The preference gives a % to sign starting with the first available signing period. So let's say he's Early and it's the very first cycle of signings. It checks to see if he has a qualifying offer (H or VH, scholly offer, available roster spot). If so then it uses a RNG to determine if he'll sign that period. Let's say first cycle it's 50% chance.
If the RNG says he doesn't sign then it goes to the next cycle but the chance that he signs increases. Not sure how much but let's say it goes up to 60%. Then if no sign then goes up to 70%, etc etc until he signs.
So for Early, they start with a much higher % while EoP1 starts a bit lower, both increase with ever subsequent cycle.
Late works the same way but starting in the 2nd session.