You have set up a demo in which multiple iframes coexist and you have had all these iframes share the same session.
In this demo, you usually change an item in one of your iframes by performing a full refresh of the iframe.
As a consequence, you notice that, sometimes, the data flow on all pages is restarted.

Is the above equivalent to your description?
This is possible with SHARE_SESSION, as closing or reloading the page that holds the Engine causes the connection to LS to be lost and the library must replace it with a new Engine and a new session.
This also affects the other pages and the starting of the new flow may be noticeable.

Is that effect causing you problems?
What do you mean by "the two iFrame suddenly refreshing"? Do you refer to a full page refresh, as though location.reload() were issued? Nothing like this should be caused by LS directly.