Time Machine backup on shared folder

I followed the procedure at https://www.macworld.com/article/3192942/macs/how-to-set-up-an-external-drive-as-a-time-machine-destination-for-multiple-macs.html to back up three laptops to a shared folder on a disk attached to my iMac (21.5, 2013).

A few days ago I had to format the internal drive of the iMac, which I did. Since then, I haven't been able to get the laptops to connect to their backups in the shared folder. First I had to repeat the procedure on the iMac, as the folder was no longer shared. Now the laptops can see the folder, but instead of using their existing backups they all start a new one.

Is there a way to get them to resume from where they had left in order not to lose older backups?

Thank you everybody for your help.