Q: Why did Touko not have any memories when she switched to her puppet body?

A: I think it is because the transition is too smooth.

Touko #1: "I am a bit tired. Time for a nap ~★"
Puppet Touko: "Oops, I dozed off for six hours instead of three ~★"

As smooth as that. Touko's puppets are stored all over the world. After one dies, the active, next-in-line Touko (puppet) will awaken. Touko (puppet) will first construct a puppet of herself, and then go outside to start her hunt for bishoujo. However, whether she inherits the will and goals of the original will depend on her location. The closer the puppet is to the original, the more likely she will inherit the original's will. If the puppet is activated from a site that is too distant, a blank in her memory proportional to the distance will form.
By the way, the puppet who awakened after Alba killed Touko disobeyed her own rule of "begin activity after constructing a puppet" and went straight for Alba. That is Touko for you, easily roused and lacks patience.

TYPE-MOON Fes. Official Pamphlet 10th Anniversary Q & A Booklet