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Searches for optical transients are usually performed with a cadence of days to weeks, optimized for supernova discovery. The optical fast transient sky is still largely unexplored, with only a few surveys to date having placed meaningful constraints on the detection of extragalactic transients evolving at sub-hour time-scales. Here, we present the results of deep searches for dim, minute-time-scale extragalactic fast transients using the Dark Energy Camera, a core facility of our all-wavelength and all-messenger Deeper, Wider, Faster programme. We used continuous 20 s exposures to systematically probe time-scales down to 1.17 min at magnitude limits g > 23 (AB), detecting hundreds of transient and variable sources. Nine candidates passed our strict criteria on duration and non-stellarity, all of which could be classified as flare stars based on deep multiband imaging. Searches for fast radio burst and gamma-ray counterparts during simultaneous multifacility observations yielded no counterparts to the optical transients. Also, no long-term variability was detected with pre-imaging and follow-up observations using the SkyMapper optical telescope. We place upper limits for minute-time-scale fast optical transient rates for a range of depths and time-scales. Finally, we demonstrate that optical g-band light-curve behaviour alone cannot discriminate between confirmed extragalactic fast transients such as prompt GRB flashes and Galactic stellar flares.