This is all "operationally correct".
If you are intrigued as to what it means for the wave function to collapse, and related questions such as at which speed does it collapse, etc, you must consider what it means to measure something.
If you want to know the property of some particle you need to interact with it ... at least with another particle. The system of those two particles is described by a wave function. This wave function evolves according to the Schrödinger equation and it will tell you that after the interaction you have a superposition of two states: one where the particle you're measuring is inside the box and the measurement probe particle is carrying that information, and the other state that tells you that the particle is outside the box *and* the measurement probe tells is carrying that information.
The wave function of the system hasn't really collapsed to a single state.
Now, let's say that your measurement apparatus records the information of this test particle by e.g. printing it out to a piece of paper or whatever (bits in hard disk)
The wave function of the whole system now captures the superposition where the measured particle was in one state and the paper contains black ink in some places and not in other places, superimposed with the other state where the measured particle was in the other state and the paper carries ink in other locations.
Nothing has collapsed yet; you just have a very complicated wave function. By processing the measurement you effectively introduced a "causality amplification" process, but one that operates on the whole of the wave function.
But, you may protest: "I see only one outcome of the measurement!"
The wave function of the universe is in a superposition of your body (and thus brain) being in a state where you have observed ( and recorded such observation) one measurement outcome and another state where you have observed the other outcome.
Both states are equally real and present in the wave function of the universe. But each of the brain states in the superposition doesn't interact with the other states do each future though you have in one of the superimposed states are effectively independent from the others, giving the impression that the wave function has "collapsed".
Some people like to say that the "universe has split" into independent world lines or something like that. Some people find this terminology helpful, some find it confusing. But the thing is, this just follows from applying the Schrödinger equation without making arbitrary exceptions when humans get involved.