Ulysses handles backups automatically. (My iPhone asked if I wanted to correct that to automagically. I was tempted.) The default setting is for Ulysses to keep hourly backups for the past 12 hours, daily backups for the past 7 days, and weekly backups for the past 6 months. You can also make a backup yourself at any time.
I’ve used Ulysses everyday for months and had no idea it was keeping Time Machine-like backups of my work. But I’m not surprised to hear that this feature exists — this type of attention to detail is the reason I chose it as my primary writing app.