I am in the reverse situation, my blood pressure has been high and I am on BP medication to keep it down. However, I was on Flowmaxtra ( tamsulosin) for my urinary with the bonus of helping lower my BP. I am now weaning off Flowmaxtra because it is not needed for my urinary but my BP is increasing so we are now re tweaking my BP medication to compensate.
Tamsulosin can have the effect of making you dizzy or faint if you get up from a chair or out of bed quickly and walk straight away. I think your heart doesn't pump the blood to your head quickly enough and you can pass out for a few seconds.
This has happened to me a couple of times, my BP was very low for a while after on both occasions. My Systolic dropped to 94 , diastolic was 53 and my heart rate was 53.
I think it is really only an issue when you are on lots of other BP medication, in particular betablockers.