There's a party. Yelling can be heard from a bathroom.
Everyone turns their attention toward the bathroom. Just then, the door bursts open and Fred comes storming out, followed by Selma.
Everyone's attention turns toward the bathroom. Just then, the door bursts open and Fred comes storming out, followed by Selma.
Are either okay?
Both are acceptable, but there is a difference. The choice of subject in English can affect how intent and cause and effect are expressed.
In "everyone turns their attention toward ...," the subject is "everyone." With the following verb, this evokes the idea of intent: that the people in question (who are the subject of the sentence) are deliberately taking an action, shifting their attention to the bathroom. The cause of the action being described originates with the people ("everyone").
On the other hand, in "everyone's attention turns toward ...," the subject is no longer the people, but their attention. The idea of intent is gone, opening this up to the idea that some external factor caused the attention to shift. The cause of the action being described originates somewhere else: in this case, with the yelling described in the preceding sentence.
Both are grammatical and idiomatic in modern U.S. English.
There is an old-fashioned view that, because “everyone” is singular, “their” should be replaced by “his,” with “his” implying nothing about sex, or by “his or her.” Some writers might subscribe to such a view, but American idiom finds “their” to be perfectly acceptable when used in a singular sense without any implication as to sex.
To avoid all this, some might prefer your second version, which simply avoids the issue of what pronoun goes with “everyone” when no implication of sex is warranted, but that is an issue of style rather than grammar.
