Now, what you've done is run ignition power into two relays' common terminals which then pass the power along to the normally closed terminals. Since the positive wire from each turn signal is connected to these normally closed terminals, the turn signal bulbs will be lit any time the ignition is switched on. When you flip on the turn signal of choice, that particular relay will be energized, then de-energized (and so on) causing the common terminal of the relay to disconnect from the normally closed terminal (87a, the one the turn signal positive wire is connected to) and connect to the normally open terminal (87, which isn't connected to anything). This effectively disconnects power from the turn signal bulb causing it to go out.
Some blinker relays (the one in your bike's fuse box) are sensitive to impedence, and if the new relays you installed as a load in place of the turn signal bulb itself have more or less resistance they may affect the frequency of the flash. If the turn signals flash too quickly (the likely scenario) you can place resisters on terminal 85 (the coil hot terminal) to more closely match the impedence of a bulb, but you probably won't have any problems.

It would be best to bind the two relays together by holding them side-by-side and wrapping them with electrical tape. You should then mount them under the seat or behind a side cover. The factory wiring usually has connectors which the signals plug into just under the seat and between the two signals. You can simply unplug the wiring there and extend those wires up to your relays using insulated spade connectors if you want the operation to be reversible.