I have successfully used the following inelegant work around to address the fact that my version of Time Machine will not delete files to make room for a backup. I too received the message that my disk was full in spite of the fact that I told it to notify me when old files were deleted.
My solution was to go to Preferences and select Time Machine. I then turned TM off. This allowed me to reformat the disc using the Disk Utility in the Utility Folder inside the Applications Folder.
Once I had Erased the disk, I could then go back to Preferences Panel and turn TM back on. For good measure (and I don't know if this is necessary or not), I deselected the disc and re-selected the disc as a backup destination for TM. It showed that the disc was empty.
I then jumped ahead of the excruciatingly boring fact that TM begins a 116 second countdown before it begins it's initial backup by selecting the BACKUP NOW option.
Everything worked fine as far as it goes. I suppose that I will have to go through this tedious process the next time the "FULL" disc message appears.
I hope this helps.
OS X Yosemite, 10.10.5, iMac (27" mid 2011), 1 GB Hard Drive, and 1 GB StoreJet Transcend Media for TM Backup destination.
PS I also found out that if I copy an older version of a TM back up to another disc (just for safe keeping) I was unable to delete that file until I turned TM off. Once TM is turned off, I seem to be able to delete anything I want.