It’s because broadly speaking the exchange rate between two countries, using monetary model of exchange rates, follows the following relationship:
$$S=\ln(m)-\ln(m_f) -(\ln(y)-\ln(y_f))+\lambda(i-i_f) $$
Where $m$ is monetary base $y$ is output and $i$ nominal interest rate. Subscript f indicates foreign country. Now from perspective of developing country (so f=USA) loosen monetary policy means that $m_f$ would expand and also $i_f$ get smaller, which would lead to appreciation of the exchange rate for developing country or if there is due to $y$ or other factors already pressure for depreciation the pressure will be lower.
The intuition is that the exchange rate must be such to bring the price levels in two countries given their respective currencies to balance and the price levels in each country depend on money supply, output and interest rates. Since all currencies can be valued only relative to each other even if the home country (here developing country) does not do anything when the foreign country (here US) increases their price level and makes their currency less valuable automatically the home currency must be strengthened as its valued only relative to the other currency.
Of course in real word non of the factors are held constant and generally developing countries face strong downward pressure on their currencies because their output is so low and many developing countries also follow quite loose monetary policy often. However, again since exchange rates are relative the looser monetary policy (that is monetary expansion) in US decreases the downward pressure on the developing currencies since now there are factors that actually strengthens their currencies (namely the larger $m_f$ and lower $i_f$.
Also generally the extra riskiness of the investments in developing countries is already priced in in the interest rates companies there have to pay which already includes risk premium. If it would not be fully included there then the difference would make the exchange rate move according to above model, so that could happen as well but that would not be dependent only on whether Fed follows loose or tight monetary policy.