Mugho Pine Sherwood Compact
It's hard to say on the basis of a couple of photos and a description. There are several needle diseases that mugo's can get. European pine sawfly is common this time of year. Or it could be something as simple as winter injury or deicing salt. Since these plants were only planted last year, they are probably stressed, making them more susceptible to diseases or environmental problems. Keep them appropriately watered and wait. Here is a good diagnostic site:
Guess I'm trying to decide if it's more likely underwatered or overwatered. Would needles turn brown if it was overwatered?
We know from flooding studies that pine partially submerged for a week or more do have die off on the underwater branches. Short of that your pines are unlikely to brown due to over watering. Of course, it depends on the type of soil they are growing in and the drainage ability. For example, clay soils hold more water for a longer time than sandy soils. Mugo pines prefer a loose well drained soil. I wonder if they were burned by the recent hot days because of the heat buildup from the rock mulch. Desiccation/drying out of the branches is more likely the problem. You might want to pull back the rock mulch so it is not touching the branches. Mugo pines are often pruned to maintain a rounded shape by removing some of the new growth; so pruning out the brown areas is okay. As noted above be on the look out for signs of disease. Stressed trees are more likely to be invaded by pests. See: http://www.mortonarb.org/trees-plants/tree-plant-descriptions/mugo-pine