Modes

Every player decides what they get after somebody kills them. The choice is theirs, kept per player by ExyliaLib's player settings, so it survives restarts and follows them across servers that share ExyliaLib's database.

The three modes

In every mode, /killcam still plays the last death while it is kept (killcam.rewatch-minutes).

The names in the middle column are mode-auto, mode-ask and mode-off in messages.yml; the same words label the choice on /settings.

The server default

killcam.default-mode in config.yml is what a player gets until they choose: AUTO by default. A player who never chose follows it, so changing it and running /killcam reload changes it for all of them at once. A player who chose something else keeps their choice; one who picked the same mode as the default is stored as following it, and moves with it.

Choosing

/killcam mode auto
/killcam mode ask
/killcam mode off

The answer confirms it: Killcam after dying » offered in chat.

The same choice is on ExyliaLib's /settings screen, as Killcam with a spyglass icon, for players with exyliakillcam.use. That screen exists only when the server turns the command on, in plugins/ExyliaLib/config.yml:

settings:
  command:
    enabled: true

See the library's player settings page. Both ways write the same value: what a player picks on one is what the other shows.

Automatic respawn

With killcam.auto-respawn on (the default), a player whose mode is AUTO and whose death got a killcam skips the death screen: they respawn on their own a tenth of a second after dying, and the killcam follows without a click. Players in ASK or OFF, and deaths that get no killcam, keep the death screen as usual.

Turn it off to keep the death screen for everybody; the killcam then starts when the player clicks Respawn, as long as that is within a minute of the death.