Mealy buhs are insidious. I have not dealt with them on begonia, but on a few other plants.
Give best care you can for begonia hralth but do continue to treat for mealies even if you arent seeing them.
I dont do rex begonia, having had a few seem difficult.
Ps a pebble tray outdoors is not doing anything. Whatever evaporates will so freely disperse into the wild blue yonder, the plant isn't benefitted.
