Not necessarily. Think about it, if we’re able to reflect on our past deeds, two things need to be there. First, we need to conceive of a ‘human history’. That we’re responsible agents in history. Second, we need to conceive of a future that we’re indeed responsible for. Neither of these actually necessitate a circular conception of time. It’s ironic because the involvement of human agency in history is actually necessitated by theology that had aimed to deny that agency.
I’ve written a short piece about human history. How it started as ‘circular’ and meaningless and how it changed to being ‘linear’ and human in the Middle Ages. Check it out if you’re interested:
A Brief History of History: Changing Historical Consciousness
How and when did humans get involved in history?
Of course our conception of time and history is vastly different today. For example, we have this idea that we can buy and sell time for money. This was an appalling idea till the rise of international trade.