Space will be reclaimed by Time Machine only using the older content from backups of the same computer. Consult this archived page from Pondini:
Time Machine will, eventually, fill all the empty space available to it before it begins deleting old backups. When multiple Macs are "competing" for the same backup space, there might be room for several months of backups for one, but only a few weeks for another. This is especially likely to happen if you start backing-up a new Mac to a drive that already has a lot of backups from another Mac. Time Machine on the new Mac will not delete backups from the other Mac(s), so when it needs space for new backups, it will delete the oldest backups from the new Mac instead.
With a Time Capsule or any network drive used as a disk for Time Machine, every computer backup is stored in its own sparse bundle disk image. This is how multiple computers can be backed up to one location. Within each sparse bundle disk image, linking is used to minimize the storage required for files or folders which have not changed between backups.
This archived page from Pondini explains how to manually delete from backups and also explains the structure.