Сначала необходимо сгруппировать, а затем отсортировать (на самом деле, вы сортируете значения):
data = [{"idprj"=>13351, "prevInicioStr"=>"21/10/2019"}, {"idprj"=>14473, "prevInicioStr"=>"22/10/2019"}, {"idprj"=>14165, "prevInicioStr"=>"23/10/2019"}, {"idprj"=>14165, "prevInicioStr"=>"23/10/2019"}, {"idprj"=>14165, "prevInicioStr"=>"28/10/2019"}, {"idprj"=>14165, "prevInicioStr"=>"28/10/2019"}, {"idprj"=>14518, "prevInicioStr"=>"29/10/2019"}, {"idprj"=>14518, "prevInicioStr"=>"29/10/2019"}, {"idprj"=>13351, "prevInicioStr"=>"05/11/2019"}, {"idprj"=>14305, "prevInicioStr"=>"06/11/2019"}, {"idprj"=>14305, "prevInicioStr"=>"08/11/2019"}, {"idprj"=>14305, "prevInicioStr"=>"13/01/2020"}]
pp data.group_by { |e| e['idprj'] }
.transform_values { |values| values.sort_by { |e| e['prevInicioStr'] } }
# {13351=>
# [{"idprj"=>13351, "prevInicioStr"=>"05/11/2019"},
# {"idprj"=>13351, "prevInicioStr"=>"21/10/2019"}],
# 14473=>[{"idprj"=>14473, "prevInicioStr"=>"22/10/2019"}],
# 14165=>
# [{"idprj"=>14165, "prevInicioStr"=>"23/10/2019"},
# {"idprj"=>14165, "prevInicioStr"=>"23/10/2019"},
# {"idprj"=>14165, "prevInicioStr"=>"28/10/2019"},
# {"idprj"=>14165, "prevInicioStr"=>"28/10/2019"}],
# 14518=>
# [{"idprj"=>14518, "prevInicioStr"=>"29/10/2019"},
# {"idprj"=>14518, "prevInicioStr"=>"29/10/2019"}],
# 14305=>
# [{"idprj"=>14305, "prevInicioStr"=>"06/11/2019"},
# {"idprj"=>14305, "prevInicioStr"=>"08/11/2019"},
# {"idprj"=>14305, "prevInicioStr"=>"13/01/2020"}]}