I think he might be referring to the B model of time which has all of space time just existing always. You have always been there reading this and time can even go backways, ignoring and cause effect and so you would be reading this before I wrote it, even if it would still be after I wrote it because time would be going backways.
It seems most physicists believe in this B model of time these days.
It is almost universal, yes. General relativity models both space and time as a unified geometry.
But you state it wrong. To say 'always' implies a time aspect that is not present. To say time goes backwards is not even wrong. And no, causes still precede effects in time.
Think of it like this. Imagine the latitude and longitude lines of the Earth, but imagine that latitude measures time and longitude measures space. Space and time together determine the geometry of the spherical Earth.
In this model, time has a 'beginning' at the South pole and an 'End' at the North pole. As we move from the South pole to the North pole, space expands out of a 'singularity' (the South pole) until the equator, when it begins to contract, until a final 'singularity' at the North pole.
We exist as decorations on this sphere. Our lives start at one time (latitude), we move around a bit, and end at another time (latitude). So, the whole of your life is in spacetime and that spacetime 'just exists' as a unified geometry.
All causality happens from the south to the north. Our consciousnesses only remember things to the South (in the past). But the more northerly part of your timeline is there 'in the future' (to the North).
Also, 'north' and 'south' only make sense on the Earth (so 'before' and 'after' only make sense within the universe). There is no 'south' of the South pole and no 'north' of the North pole. Analogously, there is no 'before' the Big Bang singularity.