AFAIK, this is never covered in ANY material (books, Pottermore, or interviews).
The only case of dual broomstick flying I can recall is the battle of Seven Potters, where such a concern wasn't discussed at all (and even that isn't clear whether it was dual. The book leaves this somewhat unclear, while the movie shows them riding separately). The closest and only evidence for tandem riding I saw was this quote:
And then a broom materialized directly above them and streaked toward the ground –
“It’s them!” screamed Hermione.
Tonks landed in a long skid that sent earth and pebbles everywhere.
“Ron was great,” said Tonks warmly, relinquishing her hold on Lupin. “Wonderful. Stunned one of the Death Eaters, straight to the head, and when you’re aiming at a moving target from a flying broom –”
Even that isn't certain, since they did a stop-over at Aunt Muriel's before coming to the Burrow.
However, as a random informed speculation - we know that a Wizard and his Wand form a sort of a bond.
It would be conceivable - although unprovable from canon - that a wizard and their broomstick may also form a bond. If (big if) that is the case, then presumably the true owner of a broomstick would be listened to over the guest rider.