Interest Rates and Inflation According to the Fischer hypothesis, nominal interest rates increase with inflation, so that the underlying real interest rate is preserved.

One might then expect that if a nation A has a higher interest rate than another nation B, then the expected inflation for nation A will be higher than that of nation B. (Assuming the real rate of interest is the same accross nations as in the international Fischer hypothesis)

However, if a nation sets its interest rates by controlling money supply, then the nation can raise their interest rates by decreasing the supply of money. Wouldn't the decrease supply of money then lead to decreased inflation, rather than the increased inflation described in the Fischer hypothesis?
The fisher hypothesis, as well as related aspects of the neutrality of money hypothesis, are typically argued only to operate in the long-run, with changes in money supply having short-run effects which are modeled with monetary disequilibrium theories.

So, a nation sells bonds in exchange for liquid assets denominated in its currency and then holds onto those assets, reducing the liquidity in their economy. As a result, at short-run levels of demand, that currency will be more highly valued than it would have been otherwise (lowered inflation). However, in the long run potential investors are presented with an incentive to lend in the currency, increasing the savings rate and lowering spending until their nominal interest rate (dependent on the amount of currency available and the spending rate) is low enough that the real interest rate is the same as it was before (assuming a constant level of expected future returns in the economy over this period).

This relies on investors only considering the real economy to be of significance in their long-run deliberations "Will future demand in this industry justify my investment and provide me with a good real rate of return down the line? If I think future inflation will be very low or negative it might just be more appropriate to hang onto my money." This is, like any model, a huge simplification, but in terms of a perfectly rational investment community (it's ok, you're allowed to laugh) it seems as though it should hold fairly well.

However, to bring this into the real world somewhat. Short-run levels of inflation and short-run levels of the spending and savings rates do not seem to be especially short run. Ordinary consumers who make up the majority of the economy take a long time to change their behaviour to bring these into an equilibrium, and shocks and government interventions and technology changes are sufficiently frequent that in effect everything stays more dynamic than monetarists would imply. Does this make the hypothesis useless? Not entirely, as an investor with no means of predicting the future accurately you could do worse than trusting it and just trying to keep your margins high in case of unpleasant surprises.

As a concise answer to your question: You're right in the short-run, the fisher hypothesis is supposed to apply to the long-run, but whether it does so accurately is virtually impossible to tease out of chaotic real world data.