You've got it right.
As you've recognized, this is dialect.
_Yawl_ \- this is a less common way of spelling the dialectical _y'all_ , which is used as the second person plural.
_Hear_ \- this is a shortened form of the expression _you hear_ , which is used in the same dialect as a rhetorical way of asking for confirmation or assent.
In more standard (but still informal) American English, the same sentence could be phrased: "You guys make sure to write to me, ok?"