The general principle of connection is this:
But according to your instructions this is how it should look like:
However, before connecting, check for yourself that in the controller the minuses of the input and output are the same, are the pluses the same i.e. is 12V DC on the controller supply as on the controller output or is it also 12V DC?
Sometimes it doesn't matter if you connect as in my diagram and sometimes it can make a difference and it all depends on what level the controller is feeding the DATA signals: whether positive to minus or negative to plus, because as you know you have to blow on a lot of things.... As you have noticed I have drawn GND through the controller as if it were the same for the input as for the output, because this is often the case.... That's why it's a good idea to go over this sometimes and put together in your head what's happening and why and how you have it at your place....
The LEDs will only light up when there is a suitable signal on the DATA line and it reaches the subsequent LED.... On the LED strip, the B1-BO line is a spare, second (BIS) DATA line should you ever have the first DI-DO line go out....
Don't get confused, because on your LEDs the plus is at the bottom and the minus (GND) is at the top and in the controller manual it is the other way around, the arrow on the LED strip shows the direction of travel of the DATA signals....
Additional question: did you also purchase the sensor - IR sensor GL-SW-001 mentioned in this link:
Link ?