Well, how long the event took in our time frame is all that matters. Secondly, from the time frame of the ripped star, the slowing due to being in the high gravity field of the black hole wouldn’t be large enough to change such a broad range as hours or days. From the perspective of the black hole, well, there isn’t one.
The event took place during one swingby of the star past the blackhole. The star appears to have come in on a hyperbolic trajectory, swung past the black hole and zipped out along the exit line of the curve, losing a lot of mass to the black hole in the process.
To figure out how long this event took, you need to know the original path of the star, its speed, the masses of the two objects. Note that there is a lot of interaction on the data. The bigger the black hole, the closer the star gets and the faster it passes by. Based on the info give, clearly the astronomers had approximate figures for all these and thus could deduce a time range in which it occurred.
Comets are routinely broken up by close approaches to the Sun. The time period for such breakups can easily be hours. But, our Sun is not a black hole. A black hole can rip far larger objects apart, like stars, if they get close enough. (Even two planets will tear each other apart if they get close enough. Google “Roche Limit.”)
If a star was moving reasonably fast, and just skimmed by the event horizon of a black hole, it could indeed be ripped apart in an hour.
It would only take centuries if that was how long it took for the star to pass by. Given that that implies distances on the scale of solar system diameters, it would be unusual for a star to be broken apart at such distances.
In short, if the star is close enough and the black hole big enough to rip it apart, it isn’t going to take long.