Yes this is a known issue For whatever reason MS decided that it should put the recovery on a diffrent drive than the OS drive if it is available. Also a big note if the recovery partition cannot be found the OS does not boot.... So when installing OS to new SSD you need to have that drive be the only drive plugged in until OS is loaded then you can plug in other drives. I do not know of a way to fix this other that to reload windows.. Maybe someone else might have an idea.
The event you describe only happens when multiple non OS drives are in the system when you install the OS. The problem the OP has is he already had an OS in his computer then added a second SSD without disconnecting the first. In this case windows sees the previous OS and creates a dual boot scenario, thus the boot menu asking which OS to boot.
In the situation you describe above, removing the old SSD would prevent the computer from booting, not show a boot menu.
@OP: You need to use a program like bcedit or easybcd to remove the old OS from the boot menu.