It sucks that the oncoming nurse handled the issue in that manner.
Honestly, I do think that report is a great learning opportunity for newer nurses; it can be helpful for someone coming behind you to mention if they see something that you could do to improve (whether it's related to following a policy or a nursing judgment call). If I'm doing something wrong (or even if my action wasn't 'wrong,' but could be done better), I'd rather have the on-coming nurse mention it than not know at all.
Unfortunately, some nurses who do this are entirely tactless, and make the off-going nurse feel like an idiot. That sucks because a) it's rude, b) it affects the confidence of newer nurses, and c) it undermines the learning experience.
What I mean to say is this: even though the nurse was a jerk, try to re-frame this as a learning opportunity. It's possible that you didn't do anything wrong. However, there are a handful of things that you could do differently in case you experience this again.
First: investigate whether or not you have a policy or standard of care about this issue. As you've seen from the responses so far, some units might call this a rapid response situation, while others think nothing of it.
Second: as @lifeatthebluffs said, if you're ever in a similar situation again, always always always try to remember to ask the provider at what point they want you to notify them again (i.e. systolic > 200? a change in symptoms?) This covers you in several ways. First, if something goes wrong with the patient, you'll cover your butt. Second, if your jerky coworker gives you a hard time, you can respond that the provider only wanted to be notified for certain parameters. Third: you don't have to waffle back and forth about bugging the provider again in the middle of the night. In a perfect world, it's best to get this ordered in writing, but in a pinch you can just note the parameters discussed when you chart that you notified the provider.
Third: if you're second-guessing something like this again, your charge nurse is a great resource. They have been around long enough to have a sixth sense about what's worth escalating and what can wait. That way, if your coworker gives you a hard time, your charge nurse can back you up (and they'll probably have a bit more clout with your grumpy colleague).
Again, I know it's hard, but try to think of this as an opportunity for improvement and learning rather than some personal failing. I don't think that you did anything wrong, but you can still turn this unpleasant experience into an opportunity to grow as a nurse.