I wanted to perform atmospheric correction using MODIS surface reflectance products for validating my atmospherically corrected images (from Landsat 8). As Landsat 8 only became available in 2013, is it safe to use MODIS data of 2013 and beyond?
Yes - you can use MODIS imagery. The MODIS sensors have been degrading a bit and as such, there are some problems there. Also, given that you don't have exactly the same bands, view angles are a bit different, vastly different spatial scale and so on, the comparison will most likely be quite noisy and as such, it may indicate that a correction that actually went well, is wrong, or the other way around.
Another option would be to compare your atmospheric correction, with the atmospheric correction that the USGS have applied to Landsat 8, which is available through EarthExplorer etc. Just look for the Landsat 8 Surface Reflectance Product. This product is generally good, but there are some spatial anomalies and such, but for comparison purposes, it should be fine.