Hmm, I just tried the same process, minus the refreshing of page1, and everything still works as normal. I do the same thing, I usually have the Pages, Templates, Fields, and front end all open in separate tabs/windows at the same time as I throw things together.
Question: how are you getting the newly created page available to you for selection if you haven't refreshed page1? If I'm editing page1 that has a pagefield in either a checkbox or select format, then create a new page in the page tree, that new page isn't available to me for selection until I either refresh page1 by using the browser refresh, or hit the Save button on page1. Is this a 2.4 feature? I'm using 2.3