As loma notes, there are many control laws that come into play with FADEC (the old hydro-mechanical controls used fewer, more basic control laws - suitable for what was basically a mechanical computer, but the concept was similar).
At or near idle, the primary control is N2 speed and burner pressure (PS3) - and control can switch between N2 and PS3 depending on the conditions. So you could have a situation where the FADEC is happily controlling to a constant N2, you turn on anti-ice which causes PS3 to drop below the minimum for the conditions so control switches to PS3, fuel is added to get PS3 back to it's minimum limit causing N2 to increase.
At power, control is typically to a commanded N1 or EPR that is based on the throttle position. So at a consistent throttle position and ambient conditions, N1/EPR will be held constant, N2 and PS3 will be allowed to vary as necessary to maintain the N1/EPR - provided they remain with limits (e.g. redline). When you turned on anti-ice, the core suddenly needed to do more work, so fuel flow and N2 increased to provide the additional anti-ice bleed while maintaining a constant N1.
This is all for steady state stuff - there is a whole other set of control laws that come into play during accel/decel transients.