In "Two Over One Game Force" by Max Hardy (1990), Hardy explicitly states that the responses of 1D, 1H and 1S over an opening of 1C are alertable (pp 297) and that the rebids of 1H, 1S and 1NT by opener after a response of 1D to a 1C opening are alertable (pp 301). This comment on page 301 suggests that opener's rebids over responders 1H call to a 1C opening are NOT alertable:
Very few of opener's rebids require an alert. These are the notable exceptions:
Note that Hardy was an Associate National Director for over 20 hears as well as an accomplished player and author, and arguably the most notable proponent of the Walsh system over the last quarter of the 20th Century.
Hardy notes in the appendix that, while a call may be natural in the meaning of the ACBL Alert and Conventions Charts, if it conveys additional agreement that the opponents cannot infer from the prior auction and a natural interpretation of the call, then SAID CALL IS ALERTABLE.