Of course you don't have to rotate original files. Also, the correct POV is that you don't move/rotate/scale images or any other graphic objects. It's coordinate system that's being transformed, and changes are cumulative. Instead of keeping track of transforms applied so far, use push/pop stack frame, returning each time to unscaled/unrotated LL page corner as 0,0.

In fact, the "image" method does save/transform(translate to X,Y and scale to WxH)/restore, because image is 1x1 box "filled" with all its pixels. So there are now several transforms and stack frames for each image. That may seem wasteful but it isn't. Be generous with "save"/"restore" calls if required. (What's wasteful is importing the same image 16 times, but it's done only for sake of illustration.)

The "translate" and "image" calls could be combined in obvious way, and you can omit centering images inside A4 boxes altogether, if they are A4 as you say.

use strict;
use warnings;
use LWP::Simple;
use PDF::API2;

use constant {
    JPG => 'jpg.jpg',
    PDF => 'pdf.pdf',
    URL => 'https://jpeg.org/images/jpeg-home.jpg',
    A4W => 595,
    A4H => 842,
    RES => 72,  # image above is at 72 dpi
};

-f JPG 
    or is_success getstore URL, JPG
    or die;

my $pdf = PDF::API2-> new;
my $page = $pdf-> page;
$page-> mediabox( 'A0' );
my $content = $page-> gfx;

for my $row ( 0 .. 3 ) {
    for my $col ( 0 .. 3 ) {
        $content-> save;
        $content-> transform(
            -translate => [ A4W + $row * A4W, $col * A4H ],
            -rotate    => 90,
        );
        my $jpeg = $pdf-> image_jpeg( JPG );
        my $w = 72 / RES * $jpeg-> width; 
        my $h = 72 / RES * $jpeg-> height;
        
        $content-> translate(( A4H - $w )/2, ( A4W - $h )/2 );
        $content-> image( $jpeg, 0, 0, 72 / RES );
        $content-> restore;
    }
}
$pdf-> saveas( 'pdf.pdf' );
[download]