Re-reading the TDA rule, your card room is right...
42: Binding Declarations / Undercalls in Turn
A: General verbal declarations in turn (such as “call” or “raise”) commit a player to the full current action. See Illustration Addendum
B: A player undercalls by declaring or pushing out less than the call amount without first declaring “call”. An undercall is a mandatory full call if made in turn facing 1) any bet heads-up or 2) the opening bet on any round multi-way. In other situations, TD’s discretion applies. The opening bet is the first chip bet of each betting round (not a check). In blind games the posted BB is the pre-flop opener. All-in buttons reduce undercall frequency (See Recommended Procedure 1). This rule governs when players must make a full call and when, at TDs discretion they may forfeit an undercall and fold. For underbets and underraises, see Rule 43.
Illustration Addendum
Example 1:
NLHE, blinds 1000-2000. Post-flop, A opens for 2000, B raises to 8000, C pushes out 2000 silently. C has undercalled B’s bet. Per Rule 42-B, because B is not the opener (A is) and the round is still multi-way, at TD’s discretion C may be required to make a full call or allowed to forfeit the 2000 undercall and fold.
Example 2:
NLHE, blinds 1000-2000. Post-flop 4 players remain. A opens for 8000, B silently puts out 2000. Per Rule 42-B, B undercalled the opening bet and must make a full call of 8000.
Example 3:
NLHE, blinds 1000-2000. Post-flop, A opens for 2000, B raises to 8000, C declares “call”. Per Rule 42-A, C has made a general verbal declaration (“call”) in turn. C is obligated to call B’s full bet of 8000.