Rate of hydrolysis of ester in presence of an acidic medium
We need to consider 4 quantities for the equilibrium reaction:

$$\ce{R1COOR2 + H2O &lt;=&gt; R1COOH + R2OH}$$


The equilibrium constant
The reaction quotient
The forward reaction rate
The reverse reaction rate


The forward reaction above is of the pseudo first order, as the professor says. 

But its rate constant depends on acidic  catalytic factors and the net reaction rate is affected by the reverse reaction rate 

The concentration of products- the organic acid and the alcohol - affects the net reaction rate by increased rate of the reverse reaction
and by shifting of the reaction quotient.

The content of a mineral acid  catalyzes the reaction, what means speeding up both reactions, therefore keeping the same equilibrium constant.(required as consequence of the energy conservation law). 

The reaction is still the pseudo first order, but the rate constant depends on concentration of the catalysing acid.

The alternative approach is considering the mineral acid as self-regenerating reagent. But it must be then evaluated as reaction chain.

The content of a mineral base decreases reverse reaction rate and shifts the reaction quotient by reacting with the organic acid. It also directly reacts with the ester.

$$\ce{R1COOR2 + OH- -&gt; R1COO- + R2OH}$$

This reaction is of the 2nd order.