Here I would talk about how restrictions activate in the worlds and what difference they have between worlds that have restrictions cause they have works about them in the homeworld and works that ditravers discovered and the info is shared to many ditravers that exceeds the world level limit.
The first type all the the especific knowledge about the world will be forgotten and only general info with be retained.
For example Roman Holiday the only knowledge that a ditravers could remember are that the female protagonist(fem mc) is someone with high social status that escape to live a simple life and then encounters the male protagonist(male mc), the male mc recognize the fem mc and tried to take advantage for his work but then after various events they enjoy each other's company but they have to separate to return to their respective responsibilities after some time they meet again in their truth identities chat woth each other and the male mc leaves.
The second type depends of the importance of the info acquired.
For example Limitless(2011) Movie. the restrictions are the name of mc(Eddie Morra), the name of Vern, the name of mc's ex-wife, the name of mc's girlfriend the name of Gennady, and the name Carlos of "Carl" Van Loon( this was because robert de niro is the actor and all the actors/actres active before 1975 are easy to recognize if ditravers work hard enough). Then there restrions in how they look as if ditravers got their names how can they not know how they look like. Next restriction the NZT-48 they obviously now the drug what it can do, Next are the locations obviously the house of the mc, where he works are included, and finally his profession is restricted as is easy to obtain this info.
Alexander by some restrictions by knowing that is a movie in the future for example he isn't trying to find Eddie Morra, He is searching for the actor Bradley Cooper, he is trying to find the location where the mc house was filmed, the drug was because at the beginning the mc is very poor but after some months he dealing with the elite so there are 2 most likely possibilities a software or a drug and knowing what Alexander knows of the world a drug is the most likely option and the profession because of the plot he knows that he wrote something to an editor an there are few profession that need an editor.