Why are the corks of some of my Muscat wines popping out?
This is generally an indication that the wine is not stable - that is, it is still fermenting, which is a defect in wines not intended to be sparkling (carbonated) wines. 

If you made the wine, and the winery bottled it, this is your problem. If the winery made and bottled the wine, I would bring it up with them, as it's their problem, and hopefully they will replace the bulging bottles.

In making wines one either has to aim for a dry wine where all the sugars have been consumed and there is nothing more for the yeast to eat, or one "stabilizes" the wine by either filtering out all the yeast or chemically "stunning" them to prevent further fermentation when bottled. Whatever method was supposed to be applied to your wine was evidently not done properly or completely, and now fermentation is continuing in the bottles and causing gas pressure, which is pushing the corks out.

If you can't get the winery to replace the bulging bottles of wine, your best bet is to refrigerate it as cold as possible without freezing it, and drink as soon as possible.