In many places where I have davened I have observed people (apparently intentionally) putting on their tallis and tefillin in a different room from where davening takes place.
I have seen this even
In places where it would likely be less comfortable to do it outside than inside (e.g. in the hallway where there's only a very small table to balance tallis bag, tefillin bag, tefillin covers, siddur, etc. while there are long tables inside the shul with plenty of space).
In times when davening has not started yet and whatever noise and motion occurs during the process of putting on tefillin would not disturb anybody (indeed many other people are putting on their tefillin inside the shul).
In a minyan near me that often gets a late start, there is one person who sometimes gets up to lead berakhos before putting on his tefillin just to get the davening started. After finishing berakhos, he takes his tefillin into a different room to put them on, then comes back.
Is there some kind of halakhic or minhagic reason for doing this? If not, why do many people prefer to put on tefillin in a different room from where the davening is going on?