The functional description is close.
First - you need to realize that the speedo turn signal bulb is not grounded.
On a stock bike, if you turn on the left signal, the left signal wiring provides power to the speedo bulb - and the speedo bulb then passes its current through the right side signals to ground. The speedo bulb doesn't pass enough current to cause the right side bulbs to lights up.
In your case, the speedo bulb is passing enough current to right side lights. This is because the original bulbs were two-23 watt bulbs - 46 watts total. That calculates out to slightly less than 4 ohms to ground. When you put on LED bulbs, the resistance to ground is much, much higher, and the current necessary to light the bulbs is now measured in milli-amps. The speedo bulb provides the milli-amps necessary to light the LED bulbs. I would've thought the speed bulb would have been a little dimmer - but maybe not . . . .
As phil71 has indicated, you can restore your speedo bulbs function with two diodes. His wiring diagram for the end solution needs to be tweaked in one place (the ends of the two diodes need to be tied together). The existing bulb is not grounded, so you'd be connecting either the blue or orange to ground, and then the other to the diodes.