Testing deleting files over a certain age

Question

I have a server running Ubuntu 20.04.3. On this server there is a process which dumps a MySQL database and then tar's the files once per day for backup purposes.

My goal is to write a script which deletes any backups that are > 30 days old.

In order to test this out I decided to set something up locally on my Macbook (running macOS Big Sur). In my Terminal I did the following:

1. Created a directory on the Desktop to test my work:

   % cd ~
   % mkdir Desktop/testfiles
   % cd Desktop/testfiles
   

2. Created 4 files:

   % touch a.txt b.txt c.txt d.txt
   

3. Modify the files created in (2) so the created/modified timestamp is different on each one. This effectively means each file has been created on a different day, e.g. touch -t 202201162300 b.txt means b.txt was created/modified on 16th January 2022. The commands I ran are below:

   % touch -t 202201152300 a.txt
   % touch -t 202201162300 b.txt
   % touch -t 202201172300 c.txt
   

The file d.txt remains with today's timestamp.

4. Check that (3) has worked:

   % ls -l                                 
   -rw-r--r--  1 a.user  staff  0 15 Jan 23:00 a.txt
   -rw-r--r--  1 a.user  staff  0 16 Jan 23:00 b.txt
   -rw-r--r--  1 a.user  staff  0 17 Jan 23:00 c.txt
   -rw-r--r--  1 a.user  staff  0 18 Jan 15:45 d.txt
   

So as per (4) each of these files was created on a different day.

If I then switch back to my home directory, cd ~ and run any of the following commands there is no output:

% find Desktop/testfiles/* -mtime +2
% find Desktop/testfiles/* -mtime +3

I assumed the output of these would be that it would find files created more than 2 and 3 days ago respectively. So the output I was assuming was for -mtime +2 would give b.txt and c.txt whereas -mtime +3 would give a.txt, b.txt and c.txt.

Am I doing something wrong here? When I read https://unix.stackexchange.com/a/112407 my understanding was that the plus (e.g. +2) is the right option because I want files "older than" 2 days, in this example. I do not think minus (e.g. -2) is appropriate in my situation unless I've misunderstood.

I also am assuming this works the same in the zsh terminal on my Mac and Ubuntu.

If I did get this to work my plan was to use this on the Ubuntu server:

% find /path/to/files/on/server/* -mtime +30 -exec rm {} \;

But I'm reluctant to use this because when I'm trying to find the appropriate files locally it's not giving me the files I expect.

Any help here would be appreciated.