a turbo does not push out pressure. it pushes out air molecules at a velocity. that velocity is faster than the engine will take in on its own. the air travels down the pipes and essentially because it's being shoved in by the turbo faster than it is pulled out by the engine it backs up. as it backs up the turbo continues to spin and positive pressure is created, or boost. once the air has backed up enough that it is at the preset level of the boost controller the wastegate opens so the turbine does not spin any faster. if there is a greater volume of piping to fill it takes longer for that buildup to occur because it needs more air molecules to fill it. thus more volume in piping increases lag
it's better to think of it in terms of air molecules than just as air. X number of air molecules fit into a tube of length Y at pressure Z, or Z=X/Y. if you increase Y you must also increase X in order to maintain the same ratio, Z, otherwise your ratio becomes smaller because the denominator becomes bigger