After getting his retainer, is a lawyer (criminal) expected to inform his client about how that retainer is being spent?

If you paid a flat fee for his services then he is not obligated to inform you of everything he has done in the sense of sending you a monthly invoice. If the 3K was a down payment against fees he should keep you informed as to what he's doing and how much it costs. Some bar associations do not sanction flat fees although most criminal attorneys use them.

I agree with Mr. Kaman, that when the fee is a flat fee, the lawyer is not obligated to submit time sheets as to what he is doing. This does not mean that the client is not entitled to an update on a regular basis as to the status of the case. I suggest that your son needs to address this issue directly with the lawyer, after a complete review of the terms of the written retainer agreement I am sure you and the attorney signed. Any ambiguities should have been worked out before you paid the fee and executed the agreement, and should now be discussed as you seem to have a difference of opinion between what you are expecting and what you say is occurring. Good luck.

DISCLAIMER
This answer does not, nor is it intended to, create an attorney-client relationship; or, constitute either legal advice or attorney advertising. Rather, given the nature of this forum, it is offered solely for information purposes, as a starting point for you to use when speaking directly to a lawyer in your State. Do not assume that the legal conclusions I mention that pertain to NJ are applicable in your State. Since the facts of each case are different, it is critical for you to consult with qualified counsel with whom information can be shared and assessed under an attorney-client privilege, so that competent advice can be obtained on which you can make informed decisions. Contact an experienced criminal defense lawyer admitted to practice in your State before making any decisions about your case.