Hall Effect Current Sensor IC Data Sheet
Yes, you have it correct, the device should be wired in series with the amplifier. 
The pins 1,2 and 3,4 are isolated from the hall sensor circuitry. They are simply a conduction path with a nominal resistance of 1.2m&Omega;, so even at 30A the maximum dissipation is only 30^2 * 0.0012 = 1.08W

Hall sensing is an isolated technique, this IC just has the current p[ath fixed rather than needing to position it over a current carrying trace as with other hall ICs

This page on Allegros site explains: