Denise - find out what class of HBP meds he's on now. I'm on Lisinopril, which is an ACE inhibitor. When it was first prescribed for me, the doc gave me a combo pill of Lisinopril with Hydrochlorothyazide (HCTZ). The HCTZ is a diuretic. Almost immediately I experienced extreme dizziness and a very rapid pulse bordering on tachycardia, like your dad. It was very disorienting and not a little frightening.
My doc didn't think the diuretic was the cause, but I insisted he modify the prescription. (My husband was on only the Lisinopril and had no adverse reaction.) When the doc changed the meds to strictly Lisinopril, no diuretic, the symptoms stopped within 24 hours.
Have your dad check this out promptly. A pulse rate that fast needs attention. Maybe he needs another class of meds, like I did. Have him chart his pulse rate so he's got hard facts for the doc. Good luck!