Is this 5 letter word really that scary?, page-41

That's becasue they keep the well bore filled up with drilling mud which has a certain specific gravity to thwart any unwanted pressure situations.
There may b occassional downhole mudlosses if any fracture zones etc r present for which they can top up the mud in the hole & maintain balance. They do monitor the returns closely & can always shut the well via the BOP.

Post-coring, they do flush out the wellbore to circulate out all the downhole fluids, cutting debris, junk from the coring bit etc and slowly Log the cored section with an MWD tool before drilling on further.

Any Oil seen in the core that's retrieved to the surface, when they layout the core barrels as it drips out, is examined for fluorescence etc (ie under UV lite & oil glows in the box), before the core is cut up and stashed off into the core basket for shipment via the support vessels to the Lab.
Hope this helps.