It happens even when I'm just playing one string and a single note. I think it's the residual vibration like you're saying but to me it doesn't sound right. Maybe I'm just too concerned that I'm not playing it right.

The string are brand new string on a brand new Fender Player strat. I'm thinking the string height might be ok as well. They seem a little high close to the bridge but I'm thinking that's normal.

I think it's just me. :-)