In times of... drought, economic austerity, poverty, disease..... these are all acceptable expressions in English. There is another concept however that you mention here: the concept of being in time. Will they get her in time=Will they arrive before the exact time that we agreed upon and planned? Can Anderson pass Parker in time to win the Indy 500? Also, we say in English that it is important to be on time, which is punctual, sticking to the scheduled timing of an event, class, or meeting. Arriving on time=getting somewhere before the time agreed upon. Example, I needed to meet Terry by the library, so I left 15 minutes so that I would get there on time. In time of.... is not said in English. It is always; "In timeS of ....political upheaval, protest, war, etc. 8]

I believe they means the same thing. It means when something is occurring. I believe the word "during" can be substituted for this expression. An example would be " in times of drought, one should attempt to conserve water". (during a drought, one should attempt to conserve water)