For observing "predictable" transient events (e.g. Gamma Ray burst or gravitational wave events), observers apply (i.e. write a proposal for peer review) for "target of opportunity" (ToO)time in advance. Typically, you might say we expect LIGO to give us 2 reasonably located, strong GW events dutring the next semester and we would like 3 hours of telescope time to follow each one of these up.
If the proposal is approved, then the ToO time can be "triggered" by the proposers at any time (up to their maximum of 2 events per semester, or whatever they got approved for), by contacting the observers who are currently at the telescope and asking them to execute the ToO observing that they asked for. The current observers programme is interrupted (and they may not be compensated for this, other than perhaps co-authorship on a paper arising from the ToO).
Totally unpredictable events like Oumuamua or a new Galactic Supernova have to rely on director's discretionary time (DDT). This is a fast track, way of getting some observing time. It is still peer-reviewed to some extent and only meritorious proposals will get any time allocated. Often a DDT proposal could be approved within 48 hours.
If something truly extraordinary happened (and I would not classify Oumuamua in this way) that required observing right now, such as for example a local supernova, then I imagine that any observer at a telescope would be happy to break off what they are doing and point whatever instruments they had at it. It should be noted though that there is a risk here. At many observatories (for example ESO) you are only supposed to observe what you said you were going to observe. Departures from this can get you into trouble. A wise observer would seek permission from observatory staff/astronomers before chasing up some object somebody phoned up and asked them to observe.
See https://www.eso.org/sci/facilities/paranal/sciops/ToO_policies.html for some more information on how these policies and procedures work at ESO.