Should you scale the FFT bins by $1/N$ where $N$ is the number of points in a transient signal?
Yes, some kind of normalization needs to be done and it's a matter of convention which one to use. To explain, let $\mathbf{F}$ be a DFT matrix containing ${\rm e}^{-\jmath 2\pi \frac{mn}{N}}$. Then you can show that $\mathbf{F} \cdot \mathbf{F}^H = N \cdot \mathbf{I}_N$. This factor $N$ needs to be accounted for. Now, you can do either of the following:


Define DFT via $\mathbf{D} = \mathbf{F} \cdot \mathbf{d} \quad \rightarrow\quad$ IDFT becomes $\mathbf{d} = \frac 1N \mathbf{F}^H \cdot \mathbf{D}$.
Define DFT via $\mathbf{D} = \frac 1N \mathbf{F} \cdot \mathbf{d} \quad \rightarrow\quad$ IDFT becomes $\mathbf{d} =  \mathbf{F}^H \cdot \mathbf{D}$.
Define DFT via $\mathbf{D} = \frac{1}{\sqrt{N}} \mathbf{F} \cdot \mathbf{d} \quad \rightarrow\quad$ IDFT becomes $\mathbf{d} = \frac{1}{\sqrt{N}} \mathbf{F}^H \cdot \mathbf{D}$.


All three of them can be used and none of them is more or less correct than the other. Matlab uses the second one, Maple the third (if I remember correctly).

If you need the units to resemble Fourier integrals, normalizing by $\Delta t$ or $\Delta f$ can make sense as well, as you found in the slide set. Depends on what you want to do with the result really.