It took several months to shift my breath to the diaphragm. The exercises certainly help with lengthening the inhale and exhale, maximizing both oxygen intake and carbon dioxide excretion.
If you have poor posture and core support and a tight chest, I would say experiment with filling your lungs completely, and with engaging your abs very slightly on the _inhale_, to feel some of the sensations of full, supported breathing. Your core muscles create pressure that helps fully inflate your lungs.
Don’t listen to any admonishments about “breathing wrong” as your body will use them to create additional tension and restriction rather than relaxation and freedom.
Assuming you're a reasonably healthy person (i.e. you don't have a chronic breathing condition like COPD), then your tidal volume isn't the limiting factor in either of those things.
Your respiratory rate is driven by the level of carbon dioxide in your blood. Your body will adjust the rate up and down to keep it at an appropriate level (this is an important tool in your body's toolbox for maintaining the correct pH of your blood). Getting rid of too much CO2 is also bad (it's why someone who is hyperventilating ends up with spasms in the hands and feet). Getting rid of CO2 requires much more air movement than is necessary to keep your blood oxygen levels up.
tl;dr; "Maximizing" those things shouldn't be a goal. Your body is already managing CO2 and O2 levels appropriately.