Why does an increased heart rate mean increased blood pressure?
In good approximation, the arterial blood pressure PA depends with

PA = PV + R x dv/dt,

on central venous pressure PV, total peripheral resistance R (also referred to as TPR or PVR) and cardiac output dv/dt (aka CO) – the usually cited equation MAP = CO * PVR is an over-simplification. Since cardiac output is defined with

dv/dt = RH * VS

as a result of heart rate (RH) and stroke volume (VS) the blood pressure should increase if heart rate increases.

However, in reality, the conditions are more complex. In exercise body temperature increases, which leads (via the thermoregulatory system) to vasodilation, so that the total peripheral resistance R decreases, which is able to reduce the blood pressure again.

Decreasing PV in exercise should occur on a very slow time-scale and only be relevant in long-time endurance training.

Concentrations of some hormones change in exercise. Levels of some stress hormones (catecholamines) rise and therefore increase cardiac output, but their action on peripheral resistance is heterogeneous. It goes up, if alpha receptors are stimulated, but decreases after stimulation of beta receptors. Similar to (and partly mediated by) beta adrenergic action classic thyroid hormones (e.g. T4, T3 and 3,5-T2) increase heart rate but decrease total peripheral resistance. It depends on the type of exercise if thyroid hormones rise or drop. They are increased in short-term or endurance exercise (representing type 2 allostasis) but decrease in exhausting exercise (leading to type 1 allostasis).

In summary, it depends on many factors, if blood pressure increases during exercise. In ergometry the blood pressure usually slightly rises.

References

1: GREENE BA. Cardiac output and total peripheral resistance in anesthesiology;
clinical applications. J Am Med Assoc. 1958 Mar 1;166(9):1003-10. PMID
13502096. https://www.ncbi.nlm.nih.gov/pubmed/13502096 https://doi.org/10.1001/jama.1958.02990090011003

2: Mayet J, Hughes A. Cardiac and vascular pathophysiology in hypertension.
Heart. 2003 Sep;89(9):1104-9. PMID 12923045. https://www.ncbi.nlm.nih.gov/pubmed/12923045/ https://doi.org/10.1136/heart.89.9.1104

3: Silva AS, Zanesco A. Physical exercise, β-adrenergic receptors, and vascular response. Jornal Vascular Brasileiro. 2010 9(2). https://doi.org/10.1590/S1677-54492010000200007

4: Chatzitomaris A, Hoermann R, Midgley JE, Hering S, Urban A, Dietrich B, Abood 
A, Klein HH, Dietrich JW. Thyroid Allostasis-Adaptive Responses of Thyrotropic
Feedback Control to Conditions of Strain, Stress, and Developmental Programming. 
Front Endocrinol (Lausanne). 2017 Jul 20;8:163. doi: 10.3389/fendo.2017.00163.. PMID 28775711. https://www.ncbi.nlm.nih.gov/pubmed/28775711 https://doi.org/10.3389/fendo.2017.00163