This brings up something I used to take note of... I was not what you might call a "charismatic JW." While I never wanted to deny the experiences others attributed to God, I was hesitant to automatically conclude that He was directly responsible for things (such as you describe) that happened--good or bad. I felt that doing so was foolish because people from many other religions experienced many of the same compelling things. We would easily pooh-pooh their experiences, while many of my fellow JWs would relate experiences that they were absolutely positive came from Jehovah. It just seemed a little disengenuous to me.
It was also clear to me that some seemed particularly given to rather mystical thinking. Please know that I believe there's a God and a devil, but some of the thought patterns seemed bizarre. Example: my good friend, who had been born in Mexico--but who has lived in the US since he was about 9 (he's now about 46)--would so often attribute things to being the direct result of demons. Once he described how he came home and found a puddle of water on his dining room table and floor. After being unable to find a roof leak or any other explanation, he concluded that it must have been the work of demons. I tried reasoning with him, "Joe, if the demons are actively involved in trying to turn people away from the worship of Jehovah, why on earth would producing a puddle in your kitchen accomplish that? You think they just decided to come in and take a demon-wizz on your table?" His reply was always something like, "You never know, Bro."
Is this a cultural thing? Another Hispanic friend of mine claims that the Latin and African-American cultures both seem infused by a preoccupation with the mystical, often concluding that things are either the direct work of either spirits or God. I don't have enough experience with it to offer an opinion.
The only thing I can offer is the scripture we've read a thousand times at 1 John 4:1... "Beloved ones, do not believe every inspired expression, but test the inspired expressions to see whether they originate with God, because many false prophets have gone forth into the world..."
Here God's Word clearly communicates that things would happen, which we might mistakenly believe to be "inspired." So if the JWs coming to your door seems like an "inspired" happening, you have both the right--as well as the responsibility to "test" it.