I don't know what the association would be with rain, but sealant coming from random spots on the rim but not the bead lock area implies a tape problem. If it's happening at the bead itself (the joint between tire and rim), too narrow tape could be a cause.
The loud pop is normal and is a good thing. The first thing to double check would be a consistent lock all the way around.
Orange works well with all the light Panaracer or Panaracer-made tires, so no this does not sound like a compatibility problem.
If you got a puncture (which is potentially likelier in the rain) and some sealant escaped in the process of sealing, you could get something like this, collecting at the rim in a way that suggests that's the leak, but it's not. The same is true if there was a puncture that the sealant wasn't quite able to fill. But that probably wouldn't be both tires, all the time.
Light tires like this can have a way of "eating" a higher amount of sealant in initial riding, and until then can lose some through the casing. It's possible this is what you're seeing. You can test that easily by using a 2mm allen or other small thin tool as a dipstick through the valve, and then re-upping as needed if there's little or no free liquid. Clean the tire off before riding so you have a fresh start. If that doesn't work then I think looking at the tape is probably the next thing, unless you're just losing it from punctures.