That actually has nothing to do with the Event. Are you familiar with Sinjoh Ruins?
To activate the Event (which is in HG/SS only), you must have the Event Arceus following you; this is the Toys 'R Us one, and an AR code exists to generate it for those who missed it (meaning literally anyone can still do the Event today). You go to the Ruins of Alph and to the main building, where a researcher bumps into you on his way out. This activates the Event.
Later on, you meet Cynthia from Sinnoh. She asks you to follow her back to the chamber. When you get there, she will NOT let you proceed until you have nothing in your party EXCEPT the Arceus. At that point, you can continue to the remainder of the event where the Dialga, Palkia, or Giratina can be selected.
Because Arceus can be the only Pokémon in your party, you are not able to influence the nature. So I cannot guarantee you a Timid one without a lot of luck after running the Event several times (it's a longish Event; I think it goes 5-10 minutes).
In this instance, barring luck, you're relying on someone who hasn't played the legendary battle in Pearl yet. I haven't even played Pearl yet (I have it used however). Even in your example, you're assuming someone has a Timid Espeon. This is about as random as replaying the Arceus Event and actually much harder because they aren't found in the wild (you'd have to breed multiple Eevee and eventually find a Timid one). So it's not that easy; if no one can come up with one, you may have to compromise somewhere.
If it helps, I can even offer mine (a clone) for free - though obviously you have to trade something, I'll let you pick whether it's one of the DWFs on your list or just something random. I have all 649 Pokémon (even a Japanese Meloetta, which was my last species to acquire), so I don't really need to have any legendaries in exchange. However, I will replay the Event a few times tomorrow (it can be replayed via another AR code) provided I don't forget, and I'll let you know if a Timid one shows up.
I see your request for a timid Palkia. Palkia is a legendary and thus is a Pokémon that is hard to acquire, and even if I am able to get a timid Palkia, I literally would have to use my Event Arceus in Gen. IV and an AR code to do the Sinjoh Ruins event over and over to be able to pull it off, then transfer it with five other Pokémon to Gen. V (Black in this case).
I can tell you I already have a Lv.1 Palkia from that same event, in addition to a "baby" Dialga and Giratina. If you can accept the one that I have, I can clone it and have it ready for you immediately.