What is the absolute latest one can arrive at a minyan and it is still considered he is davening with the minyan? Answer:- 5 minutes before time the Minyan is called for, so that when prayers commence, you are ready to commence with the Chazzan, already clad with Tallis & Tefillin.
If you don’t have enough Derech Eretz to arrive by beginning, don’t bother coming, because late arrivers simply disturb everyone else.
I have been at 1 Minyan in Geulah on Shabbos morning, and by Boruch She’omar {Nussach Ashkenaz} they lock the door, so no-one else can come in & disturb the decent people who were noble enough to come in a timely manner.
By the way, anyone whose cell phone rings during a Minyan, by definition, is not a decent person, as he is causing a disturbance of unbeleivable proportion to decent people.
Whether arriving late at a Minyan or having a cell phone ring during a Minyan:- it is an extremely difficult call of judgement to figure out who is more blatant & disturbing to the Mispallelim.