Is it recognized on the account that the Time Machine back up was set up on? I have my original account and a "test" account. (I had trouble awhile back and Mac support suggested I create a test account.) Wouldn't/shouldn't all accounts be backed up regardless of where (the account) it was backed up?
for some other problem and it could be used to compare behaviors between the actual account and the test account. It's been years since I have had to use it.