Yes that is normal. It'll ALWAYS happen as long as you have an iPhone. Best you can do is turn off cellular data for apps in the background. Also auto update for iTunes and app store to only use wifi. This is help reduce cellular usage.
I see some 5 posts a day at least where an iPhone user is talking about coming from Android or that they have never seen such "overages" in their life and that they are always at home on wifi.
This is not the case for ALL iPhones. I switch back and forth from iOS and Android all the time. I do not see any differences in data usage between the 2 platforms on my account. I have 4 lines. 2 lines always have iPhones(1 iPhone 5S and 1 iPhone 6) on them, 1 line always has a Droid Maxx on it and 1 line switches back and forth between android/iOS. I see no discernible difference in data consumption among the lines. I see no discernible difference in data consumption even on the line switching between iOS and Android. I also have NEVER turned off cellular data on any of the iPhones. The normal data consumption with all lines combined runs about 5-7 GB/month recently.
I have yet to see any runaway data usage problems on any iPhone I have ever had on my account(2 x iPhone 4S, 1 x iPhone 5, 1 x iPhone 5S and 2 x iPhone 6). Maybe I am lucky, but if this problem is so widespread you would think out of the 6 iPhones I have had on my account, at least ONE of them would have had this happen????
Of course, I have app updates only take place via wifi UNLESS I initiate an update personally. I don't stream music, I don't stream videos. I download those onto the phone either via wifi or USB connection. I occasionally watch some ESPN on my phone. I don't use video calls(Skype, Facetime, etc...).
I personally think that it all comes down to how a person uses their phones and how they have it set up for things like updating, streaming, syncing, etc.... I can see how someone with a lack of proper data managing settings could possibly see a data use increase if several updates and such were to take place around the time that their iPhone disconnected from WiFi and reverted to Mobile Data. However, I would think that once the iPhone was woken up that WiFi would reconnect.
One thing I can think of is I have "heard" iPhones turn off wifi when idle to conserve battery power and a lot of unexplained data usage happens at night. I keep my iPhone plugged in overnight. Possibly THIS prevents wifi from shutting off??? I also use my iPhone/android device as a bedside alarm clock with the display showing a clock at night, never turning off the display and preventing the phone from becoming idle. Possibly THIS prevents wifi from shutting off??? I know my iPhone is the only one on my account which has the display on all night but the other iPhones show no suspicious data usage overnight. I believe, but am not certain the other iPhones are left plugged in overnight.
Yes, I believe that, as a battery-saving feature wifi is disconnected when idle, however, I also believe you can set (if not automatic) the phone to stay "awake" while charging. Most likely this is a good reason as to why some don't experience the data drain at night.
Yes, iPhone stays connected to wifi while plugged into power and asleep. This is also when it backs up to iCloud.
TUrning cellular off in setting forces iPhone to use wifi for apps.
ios9 is supposed to use more data than previous iOS. Which is the same story Apple has sung with every iOS update, and is probably true. My sons both have iPhone 5S and the only high data use is GPS (they both work Dominoes delivery). I didn't note any big increase when the update to iOS 9 came out.
my advantage may be my router. I bought an Apple AirPort Extreme 4 years ago and it's the best router I've had. All my devices connect easily and it has the best range. I would expect Apple devices to work best together, so no surprise. But that the Apple router works well with my non Apple tech is a bonus. I even "turned" my sister, who is somewhat anti-Apple.