Yes it does. I just installed FreeBSD 12.2-RELEASE, again. The last question is would you like to reboot into the system or live CD.
The question is there, last time I ran a FreeBSD installer there may have been a "Remove install media before rebooting" message along with it.
"Next image to boot" depends on how the disk is partitioned/installed. Oldfashioned MBR you set the active partition. Newer gpt/UEFI there are a series of flags that can be set to "boot this partition".
The check for what partition to boot is done by the bios, looks at flags/partition state to determine which one to use.
Last time I installed Windows 10 from a USB install media, it explicitly said "Please remove install media".
Pretty much every OS I've ever installed (Windows 3.x, XP, 7, Solaris, different Linux distros, different BSDs) if you reboot without removing the install media or changing boot order in BIOS you wind up booting into the installer again.
The only answer I have is what I've done for as long as I can remember on every operating system install:
Hit reboot
Wait until you get to the BIOS starting
Remove the install media
Let the machine finish booting
Don't change your boot order, simply remove the install media.
Why? Because the default boot device order on almost every single BIOS I've ever run across has "hard drives" as the last thing. Removable and network boot devices come first for the sole purpose of allowing you to install to a hard drive.
For me and others I've worked with, it seems to be common sense to remove the install media after you install before or as you are rebooting.