On Friday night, a mourner, during the first 7 days, a mourner enters shul right before the recitation of Psalm 92 (Mizmor shir l'yom hashabbat).
A mourner enters the synagogue on Friday evening before Mizmor shir l'yom haShabbat (after the main part of Kabbalat Shabbat has finished).
REASON Mizmor shir is the actual starting point of Shabbat. The congregation stands and, as the mourners walk in, greets the mourners with “HaMakom yenacheim etchem b'toch she'ar aveilei tzion v'yrushalayim.
Here is what I have found online about the practice.
When the mourner davens IN shul because there isn't enough of a community to support separate minyanim, and is necessarily part of the mincha minyan count, must he leave for the Kabbalat Shabbat and then re-enter?