PERRLA automatically syncs all of your References across computers. However, PERRLA doesn't sync your papers between your computers.
PERRLA for Word (Windows & Mac) only shows you the papers on that local computer. PERRLA Online will show you all of the papers you have created in PERRLA Online on any browser you log into.
However, it is possible (if a little cumbersome) to save your papers to a cloud-storage service (like OneDrive, iCloud, or Google Drive) to sync between computers. This can be done between Windows computers or between Macs.
There is not a way to sync your papers between Windows and Mac automatically with PERRLA for Word. If you need to use Windows and Mac, we recommend you write your papers with PERRLA Online.
If you want to know how to use a cloud-storage solution to sync your papers, we have articles with instructions for Windows and Mac.