I did my own digging and found that the -mtime +1 command returns files modified >= 2 days ago. Thus, to get files >= 1 day old, -mtime +0 should be used.
Source
Currently, the mover test logs indicates that -mtime isn't used at all when "Move files that are greater than this many days old" is set to 0. This results in everything being moved. The next increment of 1 runs -mtime +1, which selects files modified >= 2 days ago.
I think this setting should be modified such that setting it to 0 omits -mtime and setting it to 1 starts at -mtime +0. The next integers should increase -mtime by 1.