Though I am writing from experiences using Synology NAS and its Linux-flavored DSM, I suspect most NAS would have similar warning mechanisms to let the users know that NAS is running out of space. Normally a warning is a welcome feature, but Time Machine is designed to work with destination drive (or volume) running out of space.
When the destination runs out of space, Time Machine starts to erase the oldest backup. It is space-heavy by design; it keeps the record of all changes made periodically. On one side, NAS is busy warning users once the Time Machine has hit the limit, while Time Machine is casually running backup as always.
DSM simply does not have options to turn off ‘low space warning’ for specific volumes. Instead it comes with a quota settings. I recommend using shared folder’s quota. In DSM 7.2, the setting is found under Control Panel > Shared Folder > Edit [shared folder] > Advanced.
Lowest setting DSM can have for low space warning per volume is 3%. That being said, it’s best not to set the quota exactly the same as the volume; give it 5% room or more. There is also some discrepancy between the allocated size for a volume and allocatable quota to a shared folder. For me, the highest quota I could set was 4% lower from the actual allocated volume space. I suspect the 4% comes from various other settings: encryption (Full Volume Encryption) or checksum.
I will report back if the quota-enabled shared folder still creates a warning. But ultimately I believe a simple on/off switch could have worked better for DSM, as more and more applications call for the use of NAS. Say, any kind of surveillance cameras, nanny cams, and pet cams at home. These kind of applications often write-over the oldest footage. Time Machine happens to be a new comer in the long line. Losing 3% of space just to avoid a warning message seems unnecessary, unless there is a technical reason why a volume should not be maxed out.
On an unrelated note, Time Machine’s encryption for sparse bundle is notorious for being time consuming. I’ve decided to use FVE on NAS and leave Time Machine data unencrypted, so that the actual encryption will be handled on the NAS, rather then having gigabytes of information encrypted from a Mac and then sent over network. I couldn’t find any documentations on potential risks of this practice; SMB protocol between the Synology NAS and Mac is 128bit encrypted, and the contents will be stored encrypted with FVE (or encrypted shared folder, by preference). Some of the older articles I could dig up suggested using an encrypted disk, instead of relying on Time Machine’s own encryption to speed up the process. Hopefully this network version will prove to be as equally practical.
Also, from my experience, I’ve learned that DSM can temporarily allocate more space to Shared Folder than the actual quota during Time Machine backup. I was hit with series of notifications that the volume is now down to 2.5% available space, when the quota was set slightly higher than 3%.
Updated December 22, 2023: added some information on DSM allowing to use more space than what Shared Folder quota is set.