I’m not aware of any third-party apps designed to do what you describe. However, I wouldn’t expect a third-party app to do significantly better than what the built-in apps are capable of.
For the “vibrate with a notification that it’s time to work on a specific task” part … I’d either use the alarm clock or the calendar. If the schedule is the same every day (weekday, etc.), then the alarm clock is perfect; just set up the alarms to repeat and you’re done. If the schedule is more complicated, create a new calendar (just to keep things organized) and create events with alerts. You can (of course) schedule repeated events this way as well.
I’m guessing that there won’t be very many different countdown timers involved. The timer app automatically remembers the last several intervals you used, and you can create an unlimited number of named favorites.
So your friend would get either the alarm or the calendar notification, open the timer, and tap on the appropriate countdown.
Maybe a third-party app could eliminate the “open the timer, and tap on the appropriate countdown” step … but is that really that much of a big deal?
I probably should add … my wife works in a clinical setting and has a bunch of alarms (using the built-in clock app) set to make sure that she’s not late to appointments, including an alarm for lunch and that sort of thing. They’re all perfectly synchronized between her phone and her watch, and the whole thing seems to work very well for her. It’s not exactly what you’re asking for for your friend, but it sounds darned close.
b&