I am also having this issue.
First PDF opens on second monitor. Second one I open will open on main laptop monitor and 3,4,5 etc the same.
Would like it to default full screen on second monitor for all PDF's.
I had the same issue, and here is the solution I found after testing and doing other web searches.
Open a PDF. Now, un-maximize the file. Move it over to the other monitor. Now, close the document WITHOUT maximizing it on the new monitor.
Now try opening a pdf. It should open on the new monitor. Maximize it, then close it again. Now, a new pdf will open on the new monitor, and it will be maximized upon opening.
So apparently the trick is to close it when it isn't maximized on whatever monitor you want it to open on. Adobe will remember whether a document was maximized or not and open another pdf in the same way, but it will only update the monitor to use when a document is closed while not maximized.