Their goal is to engage with you as early and often in the process as possible. "Starting" check-in at this point isn't much more than updating your credit card on file and setting up a PIN for MagicBand touch-to-pay purchases. The package you received was not triggered by proximity to your upcoming trip, it's triggered when you book the reservation in the first place.
Keep in mind that your old MagicBands will work at touch points in perpetuity. The only features that are affected by the battery (which has a life of approximately two years) are the long-range features, like rides that add your ride photo without the need to tap at a touch point.
If you have a jeweler's screwdriver, you can mix and match the bands from your last trip with the new ones, creating new color combinations. You could put the red puck (officially called an "icon") in a blue band, for example. I'd recommend using the newer puck, since that one will have the freshest battery.