I think the confusion is caused by words such as "everyday" and "everyone" known as COMPOUND WORDS. This is one word made by joining two or more words together (every +day / every +one). Because of this, a lot of people think that "every time" is also a compound word but it's not! Always remember to separate the two words.
A way that helps me remember this when writing is to think of Mr. Broccoli and his girlfriend, Miss. Tomato. They break up every time because they're so different. It's a sad story but they break up every time! ("break up"= leave each other)