Avoid synchronous style resolver updates from the DevTools code.

R=pfeldman, vsevik
CC=eseidel
BUG=315885

Review URL: https://codereview.chromium.org/62093003

git-svn-id: svn://svn.chromium.org/blink/trunk@161834 bbb929c8-8fbe-4397-9dbb-9b2b20218538