In a report I handed in earlier this week, my professor corrected my sentence to

日本において、金融政策の目的に関する考え方が時間を伴い、変わってきた。

from 「に伴い」. Is there a practical difference between the two? ALC shows a bunch of examples with essentially identical usage.

Here's the definition from 大辞林：

①一緒に行く。引き連れて行く、またつき従って行く。「秘書を伴って行く」「父に伴って博物館に行く」
②ある事柄に応じて生ずる。「危険を伴う手術」「人口増加に伴う住宅問題」

It seems like に and を are being used interchangeably. Is there a rule of thumb for when to use which?