That is the correct behaviour for the engine anti-icing system in the 146.
You are correct that the INTAKE LO PRESS annunciators illuminate when the engine RPM is too low to provide sufficient air for anti-icing. When the pressure in the system increases above 5psi (approx 35% N2), the INTAKE LO PRESS annunciators will extinguish, and the ENG VLV NOT SHUT annunciators will illuminate. The purpose of the latter is to quite literally inform the pilots that the engine anti-ice valves have opened (i.e. not in the shut position).
The engine anti-ice in the 146 will be operational when the four engine anti-ice switches are set to ON, and the pressure in the system is above 5psi (engine RPM above approx. 35% N2). The wing and tail anti-icing can be turned on using the OUTER WING ANT-ICE, INNER WING DE-ICE, and TAIL ANT-ICE switches on the ice protection panel.
Mark - Just Flight