When the lector proclaimed the words, "at the name of Jesus every knee should bend," everyone would genuflect.
Outside of the recitation of the Creed on the Annunciation and Christmas, there are a few times when the entire congregation would once genuflect during a reading or proclamation at Mass.
One of those times was during the Epistle (now called the Second Reading) at Mass on Palm Sunday.
It is customary to proclaim the Letter of St. Paul to the Philippians, where he writes about Jesus’ sacrifice on the cross.
he humbled himself,Philippians 2:8-10
becoming obedient to the point of death,
even death on a cross.
Because of this, God greatly exalted him
and bestowed on him the name
which is above every name,
that at the name of Jesus
every knee should bend.
Dom Prosper Gueranger explains in the Liturgical Year why Catholics would genuflect during this reading on Palm Sunday.
In obedience to the wishes of the Church, we have knelt down at those words of the Apostle where he says that every knee should bow at the Holy Name of Jesus. If there be one time of the Year, rather than an other, when the Son of God has a right to our fervent adorations, it is this Week, when we see him insulted in his Passion. Not only should his Sufferings excite us to tender compassion, we should also keenly resent the insults that are heaped upon this Jesus of ours, this God of infinite Majesty.
While this custom is not included in today’s Roman Missal, it remains a beautiful tradition that is preserved by the Extraordinary Form of the Mass.