update_option is not saving an array, but saving the string ‘Array’

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It sounds like your array isn’t being serialized before updating the option for whatever reason. Perhaps due to ajax or just your particular situation.

Try this:

// ...

$option[ 'apps' ][] = $new_app;

if( ! is_serialized( $option ) )
    $option = maybe_serialize( $option );

$data = update_option( 'vm_fbconnect', $option );

// ...