I'm not sure they'd care.
They'd care about seasons and weather, good times of day for hunting, bad times of day for predators coming after their livestock, but sub-divisions of the day for the sake of it - I don't think they'd be that interested.
Looking at UK history, the first widespread measurement of time was the bells on monastries, which announced the time to pray. The people working in the fields would stop to pray briefly then carry on.
Clocks became more important during the industrial revolution when you wanted all your workers to turn up at the same time to their shift - but what happened then was that there were sirens on the factories to announce shift change and before that there were "knocker-uppers" employed by the factory who came down streets with a long pole to tap on the bedroom windows and get people out of bed before their shift.
For completeness - the modern age of time zones only came in with the railways - when it was possible to travel fast enough that it mattered that noon in Cardiff was different from solar noon in London by a few minutes.
I've also read books by Edwin Hall for example, regarding different cultures, and even today, not everyone tracks time particularly closely. There can be a noticeable mismatch when you have a western style employer, expecting the work force all to arrive on the dot of nine - and they don't because to the minute time keeping is not something they've ever needed before.
I understand that you are not proposing to the minute time keeping, but for the entire tribe to bother about time keeping over the day doesn't strike me as plausible.
What might be plausible is timing tasks - so cooking or metal smelting for example - however, I rather suspect those can all be done on "when its ready" - you know the look or smell of something when its reached the right point for the next step.
Tracking seasons would be important - is winter coming early this year, do we need to head south yet, that kind of thing would be important.