Downs are hilly areas, the Darling Downs is a known one here - hill;hillfort. This was a Celtic town. The dun is the tun, because towns were on hilly hillforts.
Dutch tuin as garden imo is because the Dutch were not Celtic warriors with hillforts, rather people who created towns with gardens, enclosures around houses. Their towns were 'gardens', not hills/downs.
The Celtic "dun" has been equated with the Dutch "duin" or sandhill.
But "tuin" or "tun" (garden, enclosure) has no etymological relationship with this Celtic "dun" (hillford), although my quote in a former post would suggest otherwise.
And the English "town" started like this:
O.E. tun "enclosure, garden, field, yard; farm, manor; homestead, dwelling house, mansion;" later "group of houses, village.