I know that junipers prefer their soil to fully dry before watering again, but due to the rainy weather, the soil has stayed fully wet for a couple of days (not to mention the previous rainstorms). The tree seems to be thriving with beautiful coloring in its needles. The pot also seems to be draining well. Will leaving it exposed to humidity and rain for the remainder of the rainy season cause root rot?

Not per se..
Roots do not rot because they are wet. Roots rot because they have died due to e.g., not enough air coming to them. My junipers stay outdoors yearround, and I dare say they stay wet at least as long as in your place (I only water 7 months per year. The rest of the year mama nature takes care of water). So plants in a well-draining substrate should not have a problem. However, having them in way too large pots and/or dense organic substrate may cause trouble.