donning tallit and tefilin

Dear rabbis, I wonder: in my siddur, the donning of tefilin and talit has been placed after the morning brachot. But when I enter my shul, I already before starting davening, see many already have donned taefilin and tallit. When exactely you put them on? Even before Adon Olam or Yigdal?

There is a special virtue in putting on the Tefillin before entering the Bet Haknesset. Many people follow this custom and enter the Bet Knesset while their Talit and tefillin are already on them and this should be the choice time for putting on Tefillin. However, if he knows that he will be going through unclean areas the tefillin should be put on in the courtyard or entrance to the Bet Knesset. (הזוהר פרשת ואתחנן (רסה., בית יוסף אורח חיים סימן כה אות ב, שולחן ערוך אורח חיים סימן כה סעיף ב, משנה ברורה סימן כה ס"ק ח). As far as putting on the Tefillin before or after Birkot Hashachar, The Mishna B'rura says that both are acceptable.( משנה ברורה סימן כה ס"ק יג