Update "did run" from the browser process after renderer creation.

This fixes a regression in which active use of the browser stopped being
recorded as such.

BUG=432544

Review URL: https://codereview.chromium.org/719153003

Cr-Commit-Position: refs/heads/master@{#304061}
6 files changed