I don't think there is justification to assume that simply because he ordered the construction of a second Death Star, the Emperor foresaw the first one's destruction.
When the Emperor ordered the creation of the second Death Star, construction on the first had recently finished and the power of the superlaser was tested and proven (via Alderaan). They still had all they needed to work on another, perhaps even more efficiently, having learned from the first. They had the logistics worked out (as much as can be expected of a government project, at least); the designers, workers, and infrastructure was already there and waiting; and the resources were no concern for the Galactic Empire. Palpatine was power-hungry and liked using his big toys to keep everyone in line. All that considered, the timing was perfect for building a second Death Star and so, lacking evidence to the contrary, I can only conclude that said timing was the reason behind the Emperor's decision to go ahead with the second DS and Force-aided foresight of the destruction of the first likely had nothing to do with it.