How To Turn Off Private Browsing Iphone 5c

So here is how it is happening. I have new Iphone 6 & my daughter has Iphone 5c updated to ios 8.
When you double click home & it lets you sweep up to close apps.... but if you sweep right from home screen it shows an icon that says David (me) iphone 6 & if she clicks on it it shows me browsing, if I am.
I can do the same on my phone & see her browsing.
The whole family shares 1 apple ID, but each device is named differently.
We do not have family sharing activiated I dont think.
How do I fix this?

Thx

You can use other available browsers, or use private navigation in Safari, if you really want to retain the same Apple id over and over.

Just worth mentioning, but the day after I had updated to iOS 8 I was standing in the middle of Liverpool Street Station and saw a little app icon in the bottom corner.

This was a suggested app, based on popular items in the area. Freaked me out at first but now I get it I don't mind (and have switched them off for the time-being because it's technically an advert).

Having different apple ID's where only one of you is the purchaser is the way forward for solving this problem. Your kids should not have access to your Apple ID ever, so start taking security a little bit more seriously please

stop sharing the same apple id..? everyone should have their own for multiple reasons..

^this pretty much. Stop using the same appleid.

This is handoff. It's designed so that you can start browsing on your iPhone and then switch to your iPad and open up right where you left off on the phone. Since you're using a single Apple ID for everyone then you'll see this on all of your family's devices. You can turn off handoff, or, better yet, let everyone have their own Apple ID.

So here is how it is happening. I have new Iphone 6 & my daughter has Iphone 5c updated to ios 8.
When you double click home & it lets you sweep up to close apps.... but if you sweep right from home screen it shows an icon that says David (me) iphone 6 & if she clicks on it it shows me browsing, if I am.
I can do the same on my phone & see her browsing.
The whole family shares 1 apple ID, but each device is named differently.
We do not have family sharing activiated I dont think.
How do I fix this?

Thx

It's 1 Apple ID per person. you wouldn't share your personal email with the whole family, would you? (Unless it's a family email account but never mind that lol)

Apple ID is meant to be an individual thing. One for each soul. That's how it's designed.