A few days of rain does not equal overwatering. Overwatering takes weeks or months to affect the roots and then the health of the tree so unless this tree was chronically overwatered for the past month or more overwatering is unlikely to be the cause of the current state.
The problem is, those symptoms are also symptoms of several other care problems.
Underwatering directly dehydrates the plants system. The plant responds by shutting off peripheral shoots to save water loss and we see browning foliage at the top and ends of branches, moving progressively toward the plant's core. Dehydration shows up very much quicker than overwatering. A single day of dry can kill a bonsai.
In addition, junipers are know for being slow to show symptoms. It can be several weeks after the event before we see a response in junipers and many of us have forgotten, by then, that we missed a day of watering a week or so before.
Sunburn can also cause similar symptoms because foliage is directly burnt by strong UV. Plant foliage has a similar ability to our skins to produce some sort of protection against sun. Foliage (and human skin) that has been protected from sun has less natural protection. If suddenly exposed both will burn. Skin and foliage that has regular exposure develops natural protection so can stand more exposure for longer periods before damage occurs. Trees taken from a protected location (plant nursery) and put into direct sun (because everyone says junipers need full sun, right?) may burn. Gradual acclimatisation allows the foliage to develop natural sun screen. A few extra hours each day over 2-3 weeks will usually prevent sunburn. A clue to sunburn being the problem is the affected parts are usually on the top and the sunny side of the tree with the shady side and interior less affected.
The symptoms I see in the juniper, along with the few stated facts look far more like dehydration or sunburn.
You have not given any location but I'm guessing northern hemisphere which means mid-Spring and even the best growers get caught out underwatering as day length increases, temps climb and accelerated plant growth demands extra water.
Note that it is worth while adding a location to your profile because that gives additional clues to any problems and allows our experts to give advice better suited to your specific location.
I would say those few days of rain have actually saved this juniper from death rather than caused a problem.