Assuming there's no obvious explanation (e.g. sleep walking, getting up to go to the toilet, someone 'using' your phone, etc) then no, this isn't normal.
Despite the "short answer" above, it's important to appreciate that in the absence of an activity tracking device (e.g. Apple Watch, Fitbit, etc) being paired to your iPhone, then calculations are not as accurate at they could be.
At its most basic level*, a smart phone's activity measurement is performed by processing a range of calculations based on the data captured by tri-axial accelerometers. These accelerometers record acceleration in all three spatial dimensions (i.e. up/down, left/right, and forward/backward). This data is then fed into calculations to determine activities such as "steps".
Additionally, in the absence of any external fitness trackers you'll find that smartphones typically need to calculate steps in chunks and that there's a minimum number that can be reported (e.g. your iPhone isn't ever likely to tell you that you've just moved a single step, but it could say you've moved 6 steps). That's not to say it can't measure steps down to a solitary unit, just that part of the calculations involved mean that reporting figures like 6, 7, 12, 16, 137, 346, 1037, etc are possible, but not that you got up in the middle of the night and walked just two steps (because the minimum amount of data it needs to perform the calculations is such that it can't calculate just two steps on their own).
So, what all this means is that if the Health app is regularly reporting "fishy moves at night" of 10 or more steps, then either something is triggering this (sleep walking, getting up and forgetting about it, looking at the iPhone a number of times, someone else 'using' your phone, etc) or that there's some sort of 'fault' (e.g. faulty sensor(s), wrong time allocation, etc).
If the fishy timestamps are happening multiple times during the night, then it's less likely to be someone else using the phone and more likely to be you. If it's only happening once during the night and only occasionally, then it could be someone else using your phone, or just you doing something with it. However, in all scenarios it could be some sort of fault.
If it's of concern you could do some experiments to test for different scenarios, but otherwise it's probably not worth worrying about unless you're concerned with a high accuracy of step counts during these hours.
*You haven't specified your exact iPhone model, but in recent years the calculations performed have become more refined and take in data from other sources as well (e.g. gyroscope, location, compass).