Linux

I just tried your use case, and it did move the files to the correct folder.

using zsh:

 user@computer  ~  touch test.jpg
 user@computer  ~  touch test2.jpg
 user@computer  ~  mv test.jpg ./Public 
 user@computer  ~  mv test2.jpg $_
 user@computer  ~  ls ./Public 
test2.jpg  test.jpg
 user@computer  ~  

using bash:

[user@computer Public]$ mkdir test
[user@computer Public]$ ls
test  test2.jpg  test.jpg
[user@computer Public]$ mv test.jpg ./test
[user@computer Public]$ mv test2.jpg $_
[user@computer Public]$ ls
test
[user@computer Public]$ ls test/
test2.jpg  test.jpg
[user@computer Public]$ 

using bash and full path:

[user@computer Public]$ ls
test  test2.jpg  test.jpg
[user@computer Public]$ mv test.jpg /home/user/Public/test
[user@computer Public]$ mv test2.jpg $_
[user@computer Public]$ ls
test
[user@computer Public]$ ls test/
test2.jpg  test.jpg
[user@computer Public]$ 

What shell are you using? You can check it by using echo $0.

 user@computer  ~  echo $0
/usr/bin/zsh

[user@computer ~]$ echo $0
/bin/bash

I can't reproduce it, even when putting the directory path in quotes, it still simply moved the file.