My plants have a white gooey gel on the leaves. It is so caustic that it takes the paint off the windowsill. Now my orchid, placed next to one, is also getting the same thing. It happens whether the plant is left indoors or has been put outside.
It be very honest, it sounds like their is some sap loss from a nearby plant. There are several houseplants that have a caustic white sap that would fit the description you sent. Typically, they do not leak sap unless damaged, but if there was a pest infestation on the plant with the white sap, this could lead to dripping sap which could fall on other plants and the window sill.
I would check nearby plants for damage and see if they are dripping sap. Is there a plant that was near both the amaryllis and the orchid that may be dripping sap?