I watched these videos almost 10 years ago and still find them extremely useful in everyday practice. It makes me appreciate, medicine is the ultimate application of science.
Even though both hydrogen ions and bicarbonate are produced pH is defined as the amount of hydrogen ions in solution. pH does not inherently drop if you add a base, the reason it drops is when the base reacts with the hydrogen ions taking them out of the solution. i.e. in circumstances where the reaction favours H + HCO3 , these molecules will not recombine and thus there will be lots of H ions in solution (and even though there are also HCO3 ions these do not somehow subtract from the pH as the pH is the amount of H in solution). Those molecules will recombine when the reaction is favouring the H2CO3 (and when this happens H ions will be taken out of solution and the pH will rise_. I would recommend reading up on LeChatlier's principle here. I think that is where your confusion is stemming from. TLDR; depending which side of the reaction is favoured, the H and HCO3 will either want to combine, or want to stay separate. In conditions where they stay seperate there is more H in solution and a lower pH. I hope this made it a little more clear.
