A vigorous blow-off, like you're seeing, is fairly common, more so with certain styles.
You were right to pitch the whole packet, so that's not a concern. Good thinking on setting up the blow-off tube. There's another thread about this very subject going right now, and in it there is good mention of temperature control, since slightly elevated temperatures (mid 70s) can lead to more vigorous fermentations (besides the estery flavors associated with high temps for many yeasts).
If it's warm in your house, see if you can cool your wort down a little, perhaps by placing the carboy in a shallow tub of water with frozen water bottles.
Also, welcome to HBT, and congrats on making your first beer.
Fermenter 1: Best bitter (1)
Fermenter 2: Best bitter (2)
Fermenter 3: APA
Fermenter 4: APA