Your cron line issues the
shutdown command to schedule a reboot 465 minutes later – and that’s exactly what you are experiencing. To shut down the computer immediately in the given time instead, modify the cron line:
15 22 * * * root /sbin/shutdown -h now
You cannot schedule starting the computer (not restarting when it’s been off before) using cron or by any other OS means – simply because OS is not running when the command is supposed to run. However, you can mostly schedule starting the computer in firmware (BIOS) settings. The exact instructions depend on your motherboard’s firmware.
Linux computers usually maintain system clock (used by BIOS, too) in the UTC time, so take it into account when setting the start time in BIOS. Also, don’t forget to think about DST if it’s applied in your location.