To specify a display to use with X11-aware application you would either use a dedicated command line option or, if one is not available, set the
DISPLAY environment variable in-line with the command, for example the following two commands do the same thing:
xeyes --display :0
When you login via the graphical "greeter" the environment variable will be set correctly but as you are using SSH it's not being set. Depending how you're initiating the SSH connection you might be able to define some environment variables there.
I your specific case
fbi is not using X11 but is rather accessing the frame buffer directly (clue is in the name) so the above will not work, however there is a command line option to specify the frame buffer device to use. You can use this to specify the display to use as follows:
fbi -d /dev/fb0 /path/to/some/file.png