Surprisingly enough, this one isn't actually all that complicated. No, you will not be taxed twice.
Dividends are paid by the company, which in this case is domiciled in Spain. As a Spanish company, the Spanish government will take dividend witholding tax from this payment before it is paid to a foreign (i.e. non-Spanish resident) shareholder.
What's happening here is that a Spanish company is paying a dividend to a Malaysian resident. The fact that the Spanish stock was purchased in the form of an ADR from a US stock market using US dollars is actually irrelevant. The US has no claim to tax the dividend in this case.
One brave investor/blogger in Singapore even set out to prove this point by buying a Spanish ADR just before the dividend was paid. Bravo that man!