I get no difference using criterium=previous   versus   criterium=local.

Try this extended example to see the difference:

 \setuphead[section][number=no]
 \starttext
 \startchapter[title=foo]
      \placelist[section][criterium=local,order=title]
      \startsection[title={Beta}]  \input sapolsky \stopsection
      \startsection[title={Alpha}] \input sapolsky \stopsection
 \stopchapter
 \startchapter[title=bar]
      \placelist[section][criterium=local,order=title]
      \startsection[title={Alpha}] \input sapolsky \stopsection
      \startsection[title={Delta}] \input sapolsky \stopsection
 \stopchapter
 \startchapter[title=indices]
  First local:
      \placelist[section][criterium=local,order=title]
  Now previous:
      \placelist[section][criterium=previous,order=title]
 \stopchapter
 \stoptext

--
Rik