Oil prices rose fast in the 1973 and 1979 oil shocks. As oil cost more some prices in the Western world rose and this was registered as “inflation” and the Western central banks jumped to the conclusion that they had to raise the interest rates to fight this inflation.
Inflation itself is not as bad as is often claimed. Sure, Weimar type inflation where the money that you receive in the morning has lost most of its value in the evening is destabilizing. But people can very well live with a stable inflation of around 10%. Countries like Italy have industrialized and become wealthy in such circumstances.
The main job of the central banks is not to fight inflation: it is to maintain a stable environment and to prevent bubbles and the resulting disastrous boom and bust economic cycles. And there is no question of bubbles in those circumstances: the driver of those rising prices is not excessive demand but the fact that the prices of some imports are rising due to circumstances that are not related to the national economy.
One could still make the argument that the prices are rising and that those rises will result in other rises and could so cause a standard inflationary cycle: workers are demanding wage increases to correct the inflation and companies are increasing the prices of their products because their raw materials and workers cost more.
Yet there is also another mechanism at work: the terms of exchange have worsened and now the country needs to export more to pay for its imports. This will take time: new trade relations have to be established and new markets have to be conquered. It may also take some time before the newly rich countries - like the oil sheikhs in the 1970s - start spending their new wealth. Over time internal consumption may have to fall to release production capacity for the new exports. However, that will only work once the new export links have been established. Reducing demand before that time by "inflation fighting" will only drive companies into bankruptcy and reduce the capacity of the economy to make those exports.
However, it is very questionable whether rising interest rates to fight inflation is the best way to achieve those results. In the 1970s and 1980s they caused stagflation. The Western economics seemed stuck in stagflation until the mass spending of Reagonomics got it out of the swamp. It looks like the best way to address this kind of situation is to let the price hikes have their course without taking anti-inflationary measures. Initially the government might even spend more to make up for the extra money flowing over the borders - while simultaneously redirecting the economy to export more.
Interestingly we see the same discussion now in oil exporting countries and specially in Russia that immediately following the sinking oil prices saw its currency fall. As a result imports cost more in terms of the local currency and the central bank is signalling rising inflation and taking "appropriate measures" that may well be very inappropriate.