$timeout is normally what is used to run something after a digest cycle (and after the browser renders).
$timeout will cause another digest cycle to be executed after the function is executed. If your trigger does not affect anything Angular, you can set the invokeApply argument to false to avoid running another digest cycle.
If you want your callback to run before the browser renders: If code is queued using $evalAsync from a directive, it should run after the DOM has been manipulated by Angular, but before the browser renders. However, if code is queued using $evalAsync from a controller, it will run before the DOM has been manipulated by Angular (and before the browser renders). See also https://stackoverflow.com/a/17303759/215945.