The floor cleaner is leaving a soap film behind. This can happen with window cleaners as well. Because the tile already has a shiny finish, just clean it, don't try to polish it.

I use a mixure of vinegar and water to wash my tile floors and wood floors. First I vacuum, then dust mop then wash. The vinegar and water has never left any residue or film on either floor type.

Not all floor cleaners are created equal. What is it that you are using? Is it a "cleaner" or is it a "polish"? How often? It is possible that you have done "too much" to the floor and now it is time to strip all the cleaner/polish left behind. You can find products such as TSP (trisodiumphosphate) at Walmart which can be used to remove old products. You may have to do it a few times to get everything off.

Once you are down to "bare tiles" you can start again with cleaners. This should reduce the streaking for the first year or two. Once you see the streaking, you know it is time to strip it again (TSP) and off to the races once more.