It's likely that the beetle/s you saw are unrelated to the death of these Douglas firs - it's far more likely to be phytophthera ramorum infection, currently a spreading and big problem in Europe and the UK. As yet, I am not aware of any serious borer beetles, particularly not on softwood trees like fir, in Europe - Douglas Fir is susceptible to P. ramorum, there are many so affected in the UK, though the commonest victim so far is Japanese Larch. The symptoms you describe fit with phytophthera infection - lesions appear which exude or weep, often black exudate, sometimes clear and resinous in conifers, needles brown and die, branches die back as the infection spreads. Withered shoot tips occur, though if the infection started high up, you may not have noticed those.
I have no idea whether P. ramorum is notifiable in Germany, it is in the UK, but the second affected tree should be removed as soon as possible and the wood disposed of safely to try to prevent further spread. There may be local advice about disposal if it is P. ramorum - as a point of interest, Larch forests have been and currently are being ripped out in various parts of the UK (and I believe other countries) to try to contain the spread, along with large areas of wild growing rhododendron, a host plant for phytophthera.
UPDATED ANSWER: Plant death will occur, but the time that takes is variable - depends on size and susceptibility, and the fact that it may have been present for longer than the owner of a plant has realised, particularly on large trees. Once a diagnosis has been made, removal of plants is, or should be, prompt, without waiting for them to die on their own. Inspection of interior wood from a branch you've removed often reveals dark streaking.
UPDATE 2: I don't suppose you still have any wood left from the previous tree, if it's been removed, which you could inspect for signs of infection. The pattern of its dying would certainly hint at phytophthera of some description (there's more than one variety), but if you want certainty, the inspection by and advice of a qualified tree surgeon or arboriculturalist should be sought. Unless you have some local service who might be interested - in the UK, that would be the Forestry Commission Pathology Disease Diagnosis Service, or directly to DEFRA. I imagine you must have some equivalent there.
The other possibility is simple canker which has set in for some reason - either way, the end result is the same, but its quite important to establish whether or not it's a case of phytophthera of some sort. If its P. ramorum, other shrubs in your parents' garden may well be at risk, and it's still a quarantine pathogen (I just checked). Interestingly, I discover it's now becoming a major problem in the USA, where it's more difficult to establish the cause because there, they have various borer beetles that we don't have in Europe (yet, at least) which may cause similar symptoms.