One of the issues with the sideways world and the island world is that they are three years out of sync. Flight 815 just landed in the sideways world (2004), and the island world is in late 2007- early 2008.
In past seasons, when people or their minds became out of sync, they had dangerous and deadly nose bleeds. Faraday said that the person's mind was time traveling and it could not comprehend the multiple events without a constant in both time periods. It may have been a throw-away science explanation of the events as baby steps into the full physical time travel story arc to come. But the show made the point that our characters had ONE BODY and ONE MIND. When the 815ers "foomed" back into island time, there were no known duplicates still in 2007. When Desmond "flashed" to images of the future, he was still in one body on the island.
With the sideways world, we see TWO BODIES and TWO MINDS of the characters. In order to be consistent, that means the sideways story must be set in a different universe (in order to comply with our basic knowledge of human existence). "Different" universes were confirmed in the enhanced versions of earlier season episodes that clearly spelled out the significant changes that have happened in the sideways world, i.e. Jack having a son.
From a logical construct, if you have two "real" universes (parallel or a multiverse), they should be "self-contained," that their physical planes of existence (space) is different. Otherwise, you would have have two Jacks wandering the halls of one hospital.
Since both universes are separate and distinct, they should co-exist without any cross-over or "overlap."
I think their could be a continuity issue with the old Faraday explanation. The nose bleed problem dealt with individuals mentally time traveling within the same universe, but at different points in time. That was the basis of the Eloise lab rat experiment at Oxford. We are now presented with a totally different issue: an individual mentally time traveling between two universes, which are not in sync in time. One would think the mental leaps between two universes would cause not only nose bleeds but exploding heads.
The idea that sideways world is three years in the past to the events in the island world bothers me. If the Incident that happened on the island world caused chaos or a change in the sideways world, then what is the problem? The 1977 Jughead incident appeared not to harm the normal development of the sideways world characters. The 2004 815 plane crash on the island appeared not to affect the normal development of the sideways world characters. The only differences between the worlds were personal choices and not interference from forces from the other universe. Since both worlds developed independently, through personal choices to similar events, there has not been presented any compelling reason why one universe needs to "change" or interfere with the other.