And some folks use a pick (felt or plastic).
I don't think there is a "proper way" to strum; In some cases, I think it's a matter of how folks were taught, while in others it's whatever feels comfortable. I "learned" using thumb and forefinger, but have evolved to other forms, depending on the song, e.g. I use a (fleshy) thumb roll on some ballads I've rearranged. In other cases I'll pluck one string with a thumb or pinky before strumming the chord (e.g. Edelweiss - pluck_D_D); I learned the latter from a fellow band member.
One thing that was not natural for me was to vary the strum pattern from a simple DU_DU_DU_DU, e.g. D_D_DU_DU and lots of others. Some folks do this without thinking about it, but I had to practice a lot to make it happen automatically.
In most cases, I (finally) don't have to think about it, and my right hand is responding to the equivalent of muscle memory.
I'd think you and most guitar players would have a lot less trouble with any of this stuff than those of us who hadn't played a stringed instrument before picking up a uke.