OK, so you're running the same iOS version that I have on my iPhone Xs Max. But I'm not sure what you mean - the Apps at the bottom of the screen are user selectable and you can have whichever ones you want, and the only reason Safari should open up when you wake the phone would be if you were using Safari when you put the phone down last.
I'm not sure I understand exactly what is happening with your phone but if you can describe in a bit more detail perhaps I can help.
[doublepost=1540597305][/doublepost]Wait, I think I see what you mean. In safari, when you scroll a page down, the bottom of the screen shows the bar where you can open your history or bookmarks, or switch between safari windows. I'm sure that's what you're talking about.
That is just normal behavior for safari on the iPhone. The bottom bar disappears when you're scrolling through pages so it doesn't interfere with the viewing area, but if you scroll the other way then it appears.