While a rising heart rate will increase blood flow through the body, it does not necessarily correspond with an increase in the pressure of that blood flow. This is because blood vessels can increase in size (dilate) to facilitate larger quantities of blood. Even if your heart rate were to double, your normal blood pressure & high pulse may only slightly increase blood pressure.
Whelton PK, Carey RM, Aronow WS, et al. 2017 ACC/AHA/AAPA/ABC/ACPM/AGS/APhA/ASH/ASPC/NMA/PCNA guideline for the prevention, detection, evaluation, and management of high blood pressure in adults: a report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines. J Am Coll Cardiol. 2018;71(19):e127-e248. PMID: 29146535 www.ncbi.nlm.nih.gov/pubmed/29146535.