"a few hours" > takes over 24 hours.
anyway gregor insect dick guy here. i am plagued with knowledge so get ready for an infodump.

for cockroaches in particular, the testes are inside the body and produce sperm during the early stages of life then slow down. the sperm is then stored away and glued together into spermatophores, which are then discharged during copulation. spermatophores are kind of just cum balls with three layers that are shot into the female and then sort of dissolve inside her. the sperm is released through two small openings on the underside of the abdomen, connected to the duct of the phallic gland (which adds the final layer for the spermatophores as it comes out) and the ejaculatory duct, which opens out by the gonopore under the anus (the gonopore is an opening at the end of the body; in males it's for ejaculation, in females it's for egg stuff.)

for our purposes, spermatophores Could theoretically be ignored and just give gregor normal people cum for the sake of simplicity. it'd work the same, the sperm just doesn't come out in form of a layered sphere.

now, for external genitalia, there are chitinous bits surrounding the gonopore called phallomeres.

the right phallomere has two chitinous/membranous opposing plates, and a broad serrated lobe with a saw-toothed edge and two large teeth. on the posterior side it has a sickle-shaped hook. in general, this one works as the main clasping organ and hooks onto the female during copulation.

the ventral phallomere is simpler and is a little below the right phallomere. it has a large plate and bears the gonopore.

the left phallomere is kind of the main one. it has a broad base; on the extreme left side there's a long slender arm with a curved hook called a titillator. next to the titillator, there's a shorter and broader arm with a blunt hammer-like tip and a thin ridge along its length called a pseudopenis. there are three small soft lobes next to the pseudopenis, one of them has a hook and is called an asperate lobe. the duct of the phallic gland comes between the asperate lobe and the pseudopenis.

the pseudopenis enters the female gonopore and rotates 90 degrees on its own axis, it essentially functions as an additional way to hold onto the female.

the titillator enters the female's genital chamber and basically it's for what you'd do with a regular penis—thrust into a hole.

then there's a lobe which is considered the actual penis, the continuation of the ejaculatory duct and from which the spermatophores come out. though i'm not 100% sure if it's the same as the asperate lobe...? it might be but it also might not be, i really can't say for certain.

tl;dr. cockroaches have a pseudopenis with a hammer-like head which can rotate 90 degrees on its own axis to hold onto the female during sex, a hooked titillator used to thrust into the female and stimulate her, and a lobe from which the spermatophores come out and into the female, which is quickly coated with another fluid that comes out and coats the spermatophores in a third layer that hardens it.

also i have two drawn diagrams i could share if it'd make it easier to visualize or understand? up to you though.