This posting is older than 6 months and can contain outdated information.
Thanks for the info. I think that what is happening is this:
1) With an analog display, OS X may treat the display the same way as 
if it was disconnected when you put your Mac to sleep.
2) Then, when you wake up the Mac and thus the screen, OS X sends a 
notification to apps like Remote Buddy (that registered for the event 
that the screen configuration was changed) that the screen 
configuration changed. That notification is usually sent by OS X up to 
a few seconds before a resolution change actually takes place. 
Therefore, Remote Buddy will wait a couple of seconds (5 if I recall 
correctly) before requesting the current screen size and recenter its 
menu - but it won't wait as long as 15 seconds.
3) If your screen needs this long to come up, chances are that at the 
time Remote Buddy asks OS X for the current screen resolution and OS X 
returns 1 x 1 pixels (instead of f.ex. 1024 x 768). Which in turn 
makes RB re-center its menu using that data, which is at position 0 : 
0. In OS X coordinate system, 0 : 0 is located at the bottom left of 
the screen.
Does your display have a DVI input that you could connect your Mac to 
instead? Chances are this reduces wake-up time of your display - or at 
least the time needed by OS X to identify the display.
Best regards, 
Felix Schwarz