In a mortar tube, a cannon or a rifle barrel, and explosion is set off between the projectile and a solid bulkhead at one end of a tube. The explosion is not strong enough to burst the bulkhead or blow through the side of the tube, so it takes the path of least resistance and pushes the projectile out of the way (with considerable force) during its process of expansion out of the opening at the other end of the tube. The gas is contained, with only one exit, and this is what is harnessed to move the projectile.
The Alka-Seltzer rocket is not launched from a tube (imagine how high it would go if it was!) but it tossed into the air through an identical process. Imagine if you took a cannon (on a movable platform), loaded it and placed its mouth right up against the side of a cliff. When you fired it (by remote control from a safe distance), the cannonball would be forced down the tube toward the mouth, but would be stopped by the cliff face. The gas created by the explosive charge will still be expanding and seeking an outlet, and since it cannot move the ball (or the cliff), it will move the cannon.
In the Alka-Seltzer rocket, the cap is the cannonball, the canister itself is the cannon, and the firm launch platform is the cliff face. Yes, there is a large conservation of motion effect, since because the launch platform doesn't move, all of the energy is applied to the canister once the cap is blown off. But another important factor is that the firm launch surface, by stopping the cap (cannonball) before it completely separates from the canister, causes the expanding CO2 (the explosive charge) to be contained long enough to effect a large and powerful movement of the cannon (or canister).
This is somewhat similar, but not identical, to the way a rocket engine propels a rocket. In a rocket, as in a cannon, gas is rapidly generated by the burning of a highly energetic propellant within a closed-end tube that has only one outlet. In a rocket, though, the propellant undergoes a controlled burn, rather than explodes, and it passes out of the only opening in the tube through a nozzle that accelerates it to supersonic speed. The rocket moves by jet propulsion, and is not simply thrown aloft by an explosive charge. (An important distinction that seems to have been lost on a certain government agency.) So the Alka-Selter projectile (not really a rocket) is shot up into the air in the same way that a cannon shoots a cannonball, not in the same way that the Space Shuttle lifts off from the KSC.
MarkII